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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
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        {
          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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      "id": "math.algebra.abelian_group",
      "kind": "terms",
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        "concept_id": "math.algebra.abelian_group",
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      "related_native": {
        "terminology_control": {
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          "o013_o014_preferred_id": "grup abelian",
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      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
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      "unit_links": [
        {
          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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    {
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    {
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    {
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          "first_o014_unit": "",
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          "link_status": "reserved_shared_id",
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      "unit_ids": [],
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    {
      "discovery_scope": "no_first_introduction_recorded",
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          "first_o014_unit": "",
          "link_status": "reserved_shared_id",
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      },
      "unit_ids": [],
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    {
      "discovery_scope": "no_first_introduction_recorded",
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        "unmapped_unit"
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          "link_status": "reserved_shared_id",
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      "unit_ids": [],
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    {
      "discovery_scope": "no_first_introduction_recorded",
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      "discovery_scope": "no_first_introduction_recorded",
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      "unit_ids": [],
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "unit_links": [
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      },
      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
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      "unit_links": [
        {
          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
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      "unit_links": [
        {
          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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    {
      "discovery_scope": "no_first_introduction_recorded",
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      "id": "math.category.morphism",
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        "preferred_id": "morfisme",
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        "terminology_control": {
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          "first_o014_unit": "",
          "link_status": "reserved_shared_id",
          "notes": "Use morfisme unless O013 later overrides globally; ITB 2012 comparator attests morfisma",
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      "unit_ids": [],
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "id": "math.category.kernel",
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        "preferred_id": "kernel",
        "source_course_ids": "O013|O014",
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      "related_native": {
        "terminology_control": {
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          "link_status": "reserved_shared_id",
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      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
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      "unit_links": [
        {
          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "id": "math.category.cokernel",
      "kind": "terms",
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          "first_o014_unit": "o014.aljabr2.prelude.linear-algebra",
          "link_status": "reserved_shared_id",
          "notes": "O013 prerequisite",
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      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
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      "unit_links": [
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          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "id": "math.category.image",
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        "preferred_id": "citra",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.image",
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      },
      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
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      "unit_links": [
        {
          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "link_status": "o014_new",
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          "o013_o014_preferred_id": "funktor-δ",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
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      ],
      "id": "math.category.grothendieck_category",
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        "source_course_ids": "O014",
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      "related_native": {
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        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      ],
      "id": "math.homological.derived_category",
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      "related_native": {
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
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      },
      "unit_ids": [
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      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
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      ],
      "id": "math.homological.quasi_isomorphism",
      "kind": "terms",
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        "locale": "id-ID",
        "preferred_id": "kuasi-isomorfisme",
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      "related_native": {
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_new",
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          "o013_o014_preferred_id": "kuasi-isomorfisme",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.localization",
      "kind": "terms",
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        "concept_id": "math.category.localization",
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        "preferred_id": "lokalisasi kategoris",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.localization",
          "english": "categorical localization",
          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "lokalisasi kategoris",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
          "unit_id": "o014.aljabr2.prelude.homology-history",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-002"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.homological.distinguished_triangle",
      "kind": "terms",
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        "concept_id": "math.homological.distinguished_triangle",
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        "preferred_id": "segitiga terbedakan",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.distinguished_triangle",
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_provisional",
          "notes": "English gloss retained at first use; Unit 048 records the source's explicit exact-triangle alias; coordinate with O013 before shared reservation",
          "o013_o014_preferred_id": "segitiga terbedakan",
          "variants": "segitiga eksak"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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      "id": "math.homological.shift",
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        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
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      "unit_links": [
        {
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked",
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      "id": "math.homological.triangulated_category",
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          "o013_o014_preferred_id": "kategori bertriangulasi",
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      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
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    },
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      "flags": [
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        "provisional"
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      "id": "math.homotopy.cofiber_sequence",
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        "preferred_id": "barisan kofiber",
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      "related_native": {
        "terminology_control": {
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          "o013_o014_preferred_id": "barisan kofiber",
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      "unit_ids": [
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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      "id": "math.homological.octahedral_axiom",
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      "unit_ids": [
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    },
    {
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        "terminology_control": {
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      "unit_ids": [
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.simplicial.simplicial_set",
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      "related_native": {
        "terminology_control": {
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          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "himpunan simplisial",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.simplicial.simplicial_object",
      "kind": "terms",
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      "related_native": {
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          "link_status": "o014_new",
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          "o013_o014_preferred_id": "objek simplisial",
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        }
      },
      "unit_ids": [
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      "unit_links": [
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    },
    {
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        "canon_not_independently_checked",
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      "id": "math.simplicial.nerve",
      "kind": "terms",
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        "concept_id": "math.simplicial.nerve",
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        "preferred_id": "saraf",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_provisional",
          "notes": "English gloss retained at first use; avoid collision with sheaf",
          "o013_o014_preferred_id": "saraf",
          "variants": ""
        }
      },
      "unit_ids": [
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      "unit_links": [
        {
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.simplicial.dold_kan_correspondence",
      "kind": "terms",
      "native": {
        "concept_id": "math.simplicial.dold_kan_correspondence",
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        "preferred_id": "korespondensi Dold-Kan",
        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.simplicial.dold_kan_correspondence",
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "korespondensi Dold-Kan",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.category.adjoint_equivalence",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.adjoint_equivalence",
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        "preferred_id": "ekuivalensi adjoin",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.adjoint_equivalence",
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_new",
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          "o013_o014_preferred_id": "ekuivalensi adjoin",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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      "id": "math.homological.bar_construction",
      "kind": "terms",
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        "concept_id": "math.homological.bar_construction",
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        "preferred_id": "konstruksi bar",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bar_construction",
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "konstruksi bar",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
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      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
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      "id": "math.homotopy.homotopical_algebra",
      "kind": "terms",
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        "concept_id": "math.homotopy.homotopical_algebra",
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        "preferred_id": "aljabar homotopik",
        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.homotopy.homotopical_algebra",
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          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_provisional",
          "notes": "Use adjectival form to distinguish homotopical algebra from a homotopy algebra",
          "o013_o014_preferred_id": "aljabar homotopik",
          "variants": "aljabar homotopi"
        }
      },
      "unit_ids": [
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      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-002"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.ktheory.higher_k_theory",
      "kind": "terms",
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        "concept_id": "math.ktheory.higher_k_theory",
        "locale": "id-ID",
        "preferred_id": "teori K tingkat tinggi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.ktheory.higher_k_theory",
          "english": "higher K-theory",
          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "teori K tingkat tinggi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
          "unit_id": "o014.aljabr2.prelude.homology-history",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-002"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.infinity_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.infinity_category",
        "locale": "id-ID",
        "preferred_id": "kategori-∞",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.infinity_category",
          "english": "infinity-category",
          "first_o014_unit": "o014.aljabr2.prelude.homology-history",
          "link_status": "o014_provisional",
          "notes": "Typeset in TeX as kategori-$\\infty$",
          "o013_o014_preferred_id": "kategori-∞",
          "variants": "kategori tak hingga"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.homology-history"
      ],
      "unit_links": [
        {
          "title": "Sejarah Singkat Homologi",
          "unit_id": "o014.aljabr2.prelude.homology-history",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-002"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.complex",
      "kind": "terms",
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        "concept_id": "math.homological.complex",
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        "preferred_id": "kompleks",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.complex",
          "english": "complex",
          "first_o014_unit": "o014.aljabr2.prelude.linear-algebra",
          "link_status": "o014_new",
          "notes": "Generic complex first occurs in Unit 001; specialized chain and cochain forms remain separate entries",
          "o013_o014_preferred_id": "kompleks",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.linear-algebra"
      ],
      "unit_links": [
        {
          "title": "Pendahuluan - Apakah Aljabar Linear Itu?",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-001"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.homological.t_structure",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.t_structure",
        "locale": "id-ID",
        "preferred_id": "struktur-t",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.t_structure",
          "english": "t-structure",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_provisional",
          "notes": "Retain the international symbol t",
          "o013_o014_preferred_id": "struktur-t",
          "variants": "struktur t"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.representation.tilting_theory",
      "kind": "terms",
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        "concept_id": "math.representation.tilting_theory",
        "locale": "id-ID",
        "preferred_id": "teori tilting",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_provisional",
          "notes": "English technical term retained",
          "o013_o014_preferred_id": "teori tilting",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.dg_category",
      "kind": "terms",
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        "preferred_id": "kategori-dg",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
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          "english": "dg-category",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_provisional",
          "notes": "Retain the standard abbreviation dg",
          "o013_o014_preferred_id": "kategori-dg",
          "variants": "kategori dg"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.monad_theory",
      "kind": "terms",
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        "concept_id": "math.category.monad_theory",
        "locale": "id-ID",
        "preferred_id": "teori monad",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.monad_theory",
          "english": "monad theory",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "teori monad",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.higher.higher_algebra",
      "kind": "terms",
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        "concept_id": "math.higher.higher_algebra",
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        "preferred_id": "aljabar tingkat tinggi",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.higher.higher_algebra",
          "english": "higher algebra",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_provisional",
          "notes": "Both source labels retained at first use with English gloss",
          "o013_o014_preferred_id": "aljabar tingkat tinggi",
          "variants": "aljabar lanjut"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.functor_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.functor_category",
        "locale": "id-ID",
        "preferred_id": "kategori funktor",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.functor_category",
          "english": "functor category",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "kategori funktor",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.serre_quotient",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.serre_quotient",
        "locale": "id-ID",
        "preferred_id": "kuosien Serre",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.serre_quotient",
          "english": "Serre quotient",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "kuosien Serre",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.diagram_chase",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.diagram_chase",
        "locale": "id-ID",
        "preferred_id": "pengejaran diagram",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.diagram_chase",
          "english": "diagram chase",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_provisional",
          "notes": "English gloss retained at first use",
          "o013_o014_preferred_id": "pengejaran diagram",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.small_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.small_category",
        "locale": "id-ID",
        "preferred_id": "kategori kecil",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.small_category",
          "english": "small category",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "kategori kecil",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.fully_faithful",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.fully_faithful",
        "locale": "id-ID",
        "preferred_id": "penuh dan setia",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.fully_faithful",
          "english": "fully faithful",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_provisional",
          "notes": "Use the coordinated two-adjective formulation",
          "o013_o014_preferred_id": "penuh dan setia",
          "variants": "setia penuh"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.exact_embedding",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.exact_embedding",
        "locale": "id-ID",
        "preferred_id": "pembenaman eksak",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.exact_embedding",
          "english": "exact embedding",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "pembenaman eksak",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.freyd_mitchell_theorem",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.freyd_mitchell_theorem",
        "locale": "id-ID",
        "preferred_id": "teorema pembenaman Freyd-Mitchell",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.freyd_mitchell_theorem",
          "english": "Freyd-Mitchell embedding theorem",
          "first_o014_unit": "o014.aljabr2.prelude.book-purpose",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "teorema pembenaman Freyd-Mitchell",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.book-purpose"
      ],
      "unit_links": [
        {
          "title": "Tujuan Buku Ini",
          "unit_id": "o014.aljabr2.prelude.book-purpose",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-003"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "pedagogy.exercise",
      "kind": "terms",
      "native": {
        "concept_id": "pedagogy.exercise",
        "locale": "id-ID",
        "preferred_id": "latihan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "pedagogy.exercise",
          "english": "exercise",
          "first_o014_unit": "o014.aljabr2.prelude.reader-guide",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "latihan",
          "variants": "soal latihan"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.reader-guide"
      ],
      "unit_links": [
        {
          "title": "Panduan Penggunaan",
          "unit_id": "o014.aljabr2.prelude.reader-guide",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-004"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "pedagogy.hint",
      "kind": "terms",
      "native": {
        "concept_id": "pedagogy.hint",
        "locale": "id-ID",
        "preferred_id": "petunjuk",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "pedagogy.hint",
          "english": "hint",
          "first_o014_unit": "o014.aljabr2.prelude.reader-guide",
          "link_status": "o014_new",
          "notes": "Use petunjuk for source-provided exercise hints",
          "o013_o014_preferred_id": "petunjuk",
          "variants": "isyarat"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.reader-guide"
      ],
      "unit_links": [
        {
          "title": "Panduan Penggunaan",
          "unit_id": "o014.aljabr2.prelude.reader-guide",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-004"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "publishing.cross_reference",
      "kind": "terms",
      "native": {
        "concept_id": "publishing.cross_reference",
        "locale": "id-ID",
        "preferred_id": "rujuk silang",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "publishing.cross_reference",
          "english": "cross-reference",
          "first_o014_unit": "o014.aljabr2.prelude.reader-guide",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "rujuk silang",
          "variants": "referensi silang"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.reader-guide"
      ],
      "unit_links": [
        {
          "title": "Panduan Penggunaan",
          "unit_id": "o014.aljabr2.prelude.reader-guide",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-004"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "publishing.modular_writing",
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      "id": "math.algebra.zero_divisor",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.zero_divisor",
        "locale": "id-ID",
        "preferred_id": "pembagi nol",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.zero_divisor",
          "english": "zero divisor",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "pembagi nol",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.adjunction",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.adjunction",
        "locale": "id-ID",
        "preferred_id": "adjungsi",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.adjunction",
          "english": "adjunction / adjoint pair",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_provisional",
          "notes": "Source 385-397; keep adjoin kiri and adjoin kanan as compositional forms; Unit 048 uses the attested nominal variant keadjungan",
          "o013_o014_preferred_id": "adjungsi",
          "variants": "keadjungan; pasangan adjoin"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.adjunction_unit",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.adjunction_unit",
        "locale": "id-ID",
        "preferred_id": "unit",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.adjunction_unit",
          "english": "unit of an adjunction",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Indexed definition at source 399",
          "o013_o014_preferred_id": "unit",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.adjunction_counit",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.adjunction_counit",
        "locale": "id-ID",
        "preferred_id": "kounit",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.adjunction_counit",
          "english": "counit of an adjunction",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Indexed definition at source 399",
          "o013_o014_preferred_id": "kounit",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.triangle_identities",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.triangle_identities",
        "locale": "id-ID",
        "preferred_id": "identitas segitiga",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.triangle_identities",
          "english": "triangle identities",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "First textual mention at source 384; indexed definition at source 399",
          "o013_o014_preferred_id": "identitas segitiga",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.colimit",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.colimit",
        "locale": "id-ID",
        "preferred_id": "limit induktif",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.colimit",
          "english": "inductive limit / colimit",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_provisional",
          "notes": "Source 419 and 424; coordinate with the existing generic limit row",
          "o013_o014_preferred_id": "limit induktif",
          "variants": "kolimit"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.small_limit",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.small_limit",
        "locale": "id-ID",
        "preferred_id": "limit kecil",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.small_limit",
          "english": "small limit",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Indexed first use at source 426",
          "o013_o014_preferred_id": "limit kecil",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.complete_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.complete_category",
        "locale": "id-ID",
        "preferred_id": "kategori lengkap",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.complete_category",
          "english": "complete category",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Indexed first use at source 426",
          "o013_o014_preferred_id": "kategori lengkap",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.cocomplete_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.cocomplete_category",
        "locale": "id-ID",
        "preferred_id": "kategori kolengkap",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.cocomplete_category",
          "english": "cocomplete category",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Indexed first use at source 426",
          "o013_o014_preferred_id": "kategori kolengkap",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.universal_property",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.universal_property",
        "locale": "id-ID",
        "preferred_id": "sifat universal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.universal_property",
          "english": "universal property",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "First use at source 419",
          "o013_o014_preferred_id": "sifat universal",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.equalizer",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.equalizer",
        "locale": "id-ID",
        "preferred_id": "penyama",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.equalizer",
          "english": "equalizer",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_provisional",
          "notes": "First defining table at source 432-435",
          "o013_o014_preferred_id": "penyama",
          "variants": "equalizer"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.coequalizer",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.coequalizer",
        "locale": "id-ID",
        "preferred_id": "kopenyama",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.coequalizer",
          "english": "coequalizer",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_provisional",
          "notes": "First defining table at source 436-439",
          "o013_o014_preferred_id": "kopenyama",
          "variants": "koequalizer"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.product",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.product",
        "locale": "id-ID",
        "preferred_id": "produk",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.product",
          "english": "categorical product",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Object-level defining table at source 440-443",
          "o013_o014_preferred_id": "produk",
          "variants": "hasil kali"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.coproduct",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.coproduct",
        "locale": "id-ID",
        "preferred_id": "koproduk",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.coproduct",
          "english": "categorical coproduct",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Object-level defining table at source 444-447",
          "o013_o014_preferred_id": "koproduk",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.direct_sum",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.direct_sum",
        "locale": "id-ID",
        "preferred_id": "jumlah langsung",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.direct_sum",
          "english": "direct sum",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "First use at source 450",
          "o013_o014_preferred_id": "jumlah langsung",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.yoneda_embedding",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.yoneda_embedding",
        "locale": "id-ID",
        "preferred_id": "pembenaman Yoneda",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.yoneda_embedding",
          "english": "Yoneda embedding",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "First use at source 452",
          "o013_o014_preferred_id": "pembenaman Yoneda",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.terminal_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.terminal_object",
        "locale": "id-ID",
        "preferred_id": "objek terminal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.terminal_object",
          "english": "terminal object",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Defining description item at source 456; Suryanto et al. 2016 official UNDIP witness attests obyek terminal; preferred form retained",
          "o013_o014_preferred_id": "objek terminal",
          "variants": "obyek terminal"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.initial_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.initial_object",
        "locale": "id-ID",
        "preferred_id": "objek awal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.initial_object",
          "english": "initial object",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
          "notes": "Defining description item at source 457; Suryanto et al. 2016 official UNDIP witness attests obyek inisial; existing objek inisial variant and preferred form retained",
          "o013_o014_preferred_id": "objek awal",
          "variants": "objek inisial; obyek inisial"
        }
      },
      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
      ],
      "unit_links": [
        {
          "title": "Konvensi",
          "unit_id": "o014.aljabr2.prelude.conventions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-007"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.zero_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.zero_object",
        "locale": "id-ID",
        "preferred_id": "objek nol",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.zero_object",
          "english": "zero object",
          "first_o014_unit": "o014.aljabr2.prelude.conventions",
          "link_status": "o014_new",
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      "unit_ids": [
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          "o013_o014_preferred_id": "produk serat",
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      "unit_ids": [
        "o014.aljabr2.prelude.conventions"
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      "id": "math.category.subobject",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-008"
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      "unit_ids": [
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      "unit_ids": [
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          "first_o014_unit": "o014.aljabr2.chapter1.overview",
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          "notes": "",
          "o013_o014_preferred_id": "sistem multiplikatif",
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      "unit_ids": [
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          "first_o014_unit": "o014.aljabr2.chapter1.filtered-inductive-limits",
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          "notes": "Didefinisikan melalui Mor(J) berhingga; pertama pada segmen p009",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.filtered-inductive-limits"
      ],
      "unit_links": [
        {
          "title": "Limit Induktif Terfilter",
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.natural_isomorphism",
      "kind": "terms",
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        "locale": "id-ID",
        "preferred_id": "isomorfisme alami",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.natural_isomorphism",
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          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions",
          "link_status": "o014_new",
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          "o013_o014_preferred_id": "isomorfisme alami",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-015"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.left_kan_extension",
      "kind": "terms",
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        "status": "active"
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.left_kan_extension",
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          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions",
          "link_status": "o014_new",
          "notes": "Pertama pada segmen d001",
          "o013_o014_preferred_id": "ekstensi Kan kiri",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions",
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.right_kan_extension",
      "kind": "terms",
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        "concept_id": "math.category.right_kan_extension",
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        "source_course_ids": "O014",
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      "related_native": {
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          "o013_o014_preferred_id": "ekstensi Kan kanan",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-015"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.precomposition_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.precomposition_functor",
        "locale": "id-ID",
        "preferred_id": "funktor tarik balik",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.precomposition_functor",
          "english": "precomposition / pullback functor",
          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions",
          "link_status": "o014_provisional",
          "notes": "Dalam konteks kategori funktor; jelaskan prapengomposisian pada penggunaan pertama",
          "o013_o014_preferred_id": "funktor tarik balik",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-015"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.two_category",
      "kind": "terms",
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        "concept_id": "math.category.two_category",
        "locale": "id-ID",
        "preferred_id": "2-kategori",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.two_category",
          "english": "2-category",
          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions",
          "link_status": "o014_new",
          "notes": "Pertama pada segmen r001",
          "o013_o014_preferred_id": "2-kategori",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-015"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.vertical_composition",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.vertical_composition",
        "locale": "id-ID",
        "preferred_id": "komposisi vertikal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.vertical_composition",
          "english": "vertical composition",
          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions",
          "link_status": "o014_new",
          "notes": "Pertama pada segmen i001",
          "o013_o014_preferred_id": "komposisi vertikal",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-015"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.horizontal_composition",
      "kind": "terms",
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        "concept_id": "math.category.horizontal_composition",
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        "preferred_id": "komposisi horizontal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.horizontal_composition",
          "english": "horizontal composition",
          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions",
          "link_status": "o014_new",
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          "o013_o014_preferred_id": "komposisi horizontal",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-015"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.pointwise_kan_extension",
      "kind": "terms",
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        "concept_id": "math.category.pointwise_kan_extension",
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        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
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          "notes": "Pertama pada segmen p006; istilah sumber muncul dalam catatan kaki",
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          "variants": "ekstensi Kan secara titik demi titik"
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
      ],
      "unit_links": [
        {
          "title": "Ekstensi Kan",
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.preserves_kan_extension",
      "kind": "terms",
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        "concept_id": "math.category.preserves_kan_extension",
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        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.preserves_kan_extension",
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          "o013_o014_preferred_id": "mempertahankan ekstensi Kan",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions"
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      "unit_links": [
        {
          "title": "Ekstensi Kan",
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.sheaf.presheaf",
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      "unit_ids": [
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      "unit_links": [
        {
          "title": "Konstruksi Ekstensi Kan melalui Limit",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions-as-limits",
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.sheaf.direct_image",
      "kind": "terms",
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        "concept_id": "math.sheaf.direct_image",
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        "preferred_id": "citra langsung",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.sheaf.direct_image",
          "english": "direct image",
          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions-as-limits",
          "link_status": "o014_provisional",
          "notes": "Dalam konteks funktor praberkas; pertama pada segmen e001",
          "o013_o014_preferred_id": "citra langsung",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions-as-limits"
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      "unit_links": [
        {
          "title": "Konstruksi Ekstensi Kan melalui Limit",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions-as-limits",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-016"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
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      "id": "math.sheaf.inverse_image",
      "kind": "terms",
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        "concept_id": "math.sheaf.inverse_image",
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        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.sheaf.inverse_image",
          "english": "inverse image",
          "first_o014_unit": "o014.aljabr2.chapter1.kan-extensions-as-limits",
          "link_status": "o014_provisional",
          "notes": "Dalam konteks funktor praberkas; pertama pada segmen e001",
          "o013_o014_preferred_id": "citra invers",
          "variants": "citra balik|prabayang"
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.kan-extensions-as-limits"
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      "unit_links": [
        {
          "title": "Konstruksi Ekstensi Kan melalui Limit",
          "unit_id": "o014.aljabr2.chapter1.kan-extensions-as-limits",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-016"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.localization_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.localization_functor",
        "locale": "id-ID",
        "preferred_id": "funktor lokalisasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.localization_functor",
          "english": "localization functor",
          "first_o014_unit": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "link_status": "o014_new",
          "notes": "Pertama pada segmen d001",
          "o013_o014_preferred_id": "funktor lokalisasi",
          "variants": ""
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.gabriel-zisman-localization"
      ],
      "unit_links": [
        {
          "title": "Lokalisasi Gabriel--Zisman",
          "unit_id": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-017"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.category.essential_image",
      "kind": "terms",
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        "concept_id": "math.category.essential_image",
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        "preferred_id": "citra esensial",
        "source_course_ids": "O014",
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        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "link_status": "o014_new",
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          "o013_o014_preferred_id": "citra esensial",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.gabriel-zisman-localization"
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      "unit_links": [
        {
          "title": "Lokalisasi Gabriel--Zisman",
          "unit_id": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-017"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.left_multiplicative_system",
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        "concept_id": "math.category.left_multiplicative_system",
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        "source_course_ids": "O014",
        "status": "active"
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      "related_native": {
        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "link_status": "o014_new",
          "notes": "Subtipe sistem multiplikatif; arah pecahan dan diagram bergantung padanya",
          "o013_o014_preferred_id": "sistem multiplikatif kiri",
          "variants": ""
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.gabriel-zisman-localization"
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      "unit_links": [
        {
          "title": "Lokalisasi Gabriel--Zisman",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-017"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.right_multiplicative_system",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.right_multiplicative_system",
        "locale": "id-ID",
        "preferred_id": "sistem multiplikatif kanan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.right_multiplicative_system",
          "english": "right multiplicative system",
          "first_o014_unit": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "link_status": "o014_new",
          "notes": "Subtipe sistem multiplikatif; arah pecahan dan diagram bergantung padanya",
          "o013_o014_preferred_id": "sistem multiplikatif kanan",
          "variants": ""
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      },
      "unit_ids": [
        "o014.aljabr2.chapter1.gabriel-zisman-localization"
      ],
      "unit_links": [
        {
          "title": "Lokalisasi Gabriel--Zisman",
          "unit_id": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-017"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
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      "id": "math.category.calculus_of_fractions",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.calculus_of_fractions",
        "locale": "id-ID",
        "preferred_id": "kalkulus pecahan",
        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.calculus_of_fractions",
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          "first_o014_unit": "o014.aljabr2.chapter1.gabriel-zisman-localization",
          "link_status": "o014_provisional",
          "notes": "Digunakan untuk konstruksi lokalisasi dengan pecahan",
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      "unit_ids": [
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        {
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    {
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      "flags": [
        "canon_not_independently_checked",
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        {
          "title": "Teorema Funktor Adjoin",
          "unit_id": "o014.aljabr2.chapter1.adjoint-functor-theorem",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "kind": "terms",
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        "concept_id": "math.category.well_copowered_category",
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          "link_status": "o014_new",
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      "unit_ids": [
        "o014.aljabr2.chapter1.adjoint-functor-theorem"
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      "unit_links": [
        {
          "title": "Teorema Funktor Adjoin",
          "unit_id": "o014.aljabr2.chapter1.adjoint-functor-theorem",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter1-unit-019"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        {
          "title": "Teorema Funktor Adjoin",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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      "id": "math.topology.stone_cech_compactification",
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        "concept_id": "math.topology.stone_cech_compactification",
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        "terminology_control": {
          "concept_id": "math.topology.stone_cech_compactification",
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        {
          "title": "Teorema Funktor Adjoin",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "title": "Kategori Abelian",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "o013_o014_preferred_id": "rantai menurun",
          "variants": "rantai turun"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.glimpse-of-lattice-theory"
      ],
      "unit_links": [
        {
          "title": "Sekilas tentang Teori Kisi",
          "unit_id": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-024"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.order.noetherian",
      "kind": "terms",
      "native": {
        "concept_id": "math.order.noetherian",
        "locale": "id-ID",
        "preferred_id": "Noetherian",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.order.noetherian",
          "english": "Noetherian",
          "first_o014_unit": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
          "link_status": "o014_new",
          "notes": "Tidak mempunyai rantai naik tak hingga",
          "o013_o014_preferred_id": "Noetherian",
          "variants": "kondisi Noether"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.glimpse-of-lattice-theory"
      ],
      "unit_links": [
        {
          "title": "Sekilas tentang Teori Kisi",
          "unit_id": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-024"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.order.artinian",
      "kind": "terms",
      "native": {
        "concept_id": "math.order.artinian",
        "locale": "id-ID",
        "preferred_id": "Artinian",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.order.artinian",
          "english": "Artinian",
          "first_o014_unit": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
          "link_status": "o014_new",
          "notes": "Tidak mempunyai rantai menurun tak hingga",
          "o013_o014_preferred_id": "Artinian",
          "variants": "kondisi Artin"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.glimpse-of-lattice-theory"
      ],
      "unit_links": [
        {
          "title": "Sekilas tentang Teori Kisi",
          "unit_id": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-024"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.order.finite_length",
      "kind": "terms",
      "native": {
        "concept_id": "math.order.finite_length",
        "locale": "id-ID",
        "preferred_id": "berpanjang hingga",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.order.finite_length",
          "english": "finite length",
          "first_o014_unit": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
          "link_status": "o014_new",
          "notes": "Sekaligus Artinian dan Noetherian",
          "o013_o014_preferred_id": "berpanjang hingga",
          "variants": "panjang hingga"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.glimpse-of-lattice-theory"
      ],
      "unit_links": [
        {
          "title": "Sekilas tentang Teori Kisi",
          "unit_id": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-024"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.idempotent",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.idempotent",
        "locale": "id-ID",
        "preferred_id": "idempoten",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.idempotent",
          "english": "idempotent",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Unsur e dengan e kuadrat sama dengan e",
          "o013_o014_preferred_id": "idempoten",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.karoubian_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.karoubian_category",
        "locale": "id-ID",
        "preferred_id": "kategori Karoubi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.karoubian_category",
          "english": "Karoubian category",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Kategori-Ab berobjek nol tempat setiap idempoten mempunyai kernel",
          "o013_o014_preferred_id": "kategori Karoubi",
          "variants": "kategori Karoubian"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.pseudoabelian_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.pseudoabelian_category",
        "locale": "id-ID",
        "preferred_id": "kategori pseudoabelian",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.pseudoabelian_category",
          "english": "pseudo-abelian category",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Sinonim sumber untuk kategori Karoubi",
          "o013_o014_preferred_id": "kategori pseudoabelian",
          "variants": "kategori pseudo-Abel"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.split_short_exact_sequence",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.split_short_exact_sequence",
        "locale": "id-ID",
        "preferred_id": "barisan eksak pendek terbelah",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.split_short_exact_sequence",
          "english": "split short exact sequence",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Barisan eksak pendek yang memenuhi kondisi pemisahan ekuivalen",
          "o013_o014_preferred_id": "barisan eksak pendek terbelah",
          "variants": "barisan eksak pendek split"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.section",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.section",
        "locale": "id-ID",
        "preferred_id": "penampang",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.section",
          "english": "section",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Morfisme s dengan g s sama dengan identitas",
          "o013_o014_preferred_id": "penampang",
          "variants": "seksi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.retraction",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.retraction",
        "locale": "id-ID",
        "preferred_id": "retraksi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.retraction",
          "english": "retraction",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Morfisme r dengan r f sama dengan identitas",
          "o013_o014_preferred_id": "retraksi",
          "variants": "retrakt"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.double_chain",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.double_chain",
        "locale": "id-ID",
        "preferred_id": "rantai ganda",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.double_chain",
          "english": "double chain",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Pasangan rantai epi dan mono antara objek berturutan",
          "o013_o014_preferred_id": "rantai ganda",
          "variants": "rantai bi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.double_chain_condition",
      "kind": "terms",
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        "concept_id": "math.category.double_chain_condition",
        "locale": "id-ID",
        "preferred_id": "syarat rantai ganda",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.double_chain_condition",
          "english": "bi-chain condition",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Kestabilan eventual bagi kedua arah rantai ganda",
          "o013_o014_preferred_id": "syarat rantai ganda",
          "variants": "kondisi rantai ganda"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.nilpotent",
      "kind": "terms",
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        "concept_id": "math.algebra.nilpotent",
        "locale": "id-ID",
        "preferred_id": "nilpoten",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.nilpotent",
          "english": "nilpotent",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Suatu pangkat positif sama dengan nol",
          "o013_o014_preferred_id": "nilpoten",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.local_ring",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.local_ring",
        "locale": "id-ID",
        "preferred_id": "gelanggang lokal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.local_ring",
          "english": "local ring",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Unsur tak invertibel tertutup terhadap penjumlahan",
          "o013_o014_preferred_id": "gelanggang lokal",
          "variants": "ring lokal"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.fitting_lemma",
      "kind": "terms",
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        "concept_id": "math.category.fitting_lemma",
        "locale": "id-ID",
        "preferred_id": "Lema Fitting",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.fitting_lemma",
          "english": "Fitting lemma",
          "first_o014_unit": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "link_status": "o014_new",
          "notes": "Bentuk kategori abelian di bawah syarat rantai ganda",
          "o013_o014_preferred_id": "Lema Fitting",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
      ],
      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
          "unit_id": "o014.aljabr2.chapter2.direct-sum-decomposition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-025"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.subobject_intersection",
      "kind": "terms",
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        "concept_id": "math.category.subobject_intersection",
        "locale": "id-ID",
        "preferred_id": "irisan subobjek",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.subobject_intersection",
          "english": "intersection of subobjects",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Infimum keluarga subobjek ketika ada",
          "o013_o014_preferred_id": "irisan subobjek",
          "variants": "perpotongan subobjek"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.subobject_sum",
      "kind": "terms",
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        "concept_id": "math.category.subobject_sum",
        "locale": "id-ID",
        "preferred_id": "jumlah subobjek",
        "source_course_ids": "O014",
        "status": "active"
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.subobject_sum",
          "english": "sum of subobjects",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Supremum keluarga subobjek ketika ada",
          "o013_o014_preferred_id": "jumlah subobjek",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.increasing_union",
      "kind": "terms",
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        "concept_id": "math.category.increasing_union",
        "locale": "id-ID",
        "preferred_id": "gabungan naik",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.increasing_union",
          "english": "increasing union",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Notasi gabungan bagi supremum keluarga subobjek terfilter yang menaik",
          "o013_o014_preferred_id": "gabungan naik",
          "variants": "gabungan meningkat; gabungan menaik"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.subobject_preimage",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.subobject_preimage",
        "locale": "id-ID",
        "preferred_id": "prabayang subobjek",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.subobject_preimage",
          "english": "preimage of a subobject",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Dibedakan dari funktor citra invers pada praberkas",
          "o013_o014_preferred_id": "prabayang subobjek",
          "variants": "citra invers subobjek; citra balik subobjek"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.canonical_isomorphism",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.canonical_isomorphism",
        "locale": "id-ID",
        "preferred_id": "isomorfisme kanonik",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.canonical_isomorphism",
          "english": "canonical isomorphism",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Bentuk komposisional dari isomorfisme dan sifat kanonik",
          "o013_o014_preferred_id": "isomorfisme kanonik",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.antidiagonal_morphism",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.antidiagonal_morphism",
        "locale": "id-ID",
        "preferred_id": "morfisme antidiagonal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.antidiagonal_morphism",
          "english": "antidiagonal morphism",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Morfisme ke biproduk dengan komponen pertama bertanda negatif",
          "o013_o014_preferred_id": "morfisme antidiagonal",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.order.order_reversing_bijection",
      "kind": "terms",
      "native": {
        "concept_id": "math.order.order_reversing_bijection",
        "locale": "id-ID",
        "preferred_id": "bijeksi pembalik urutan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.order.order_reversing_bijection",
          "english": "order-reversing bijection",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Korespondensi subobjek dengan objek kuosien",
          "o013_o014_preferred_id": "bijeksi pembalik urutan",
          "variants": "bijeksi yang membalik urutan"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.isomorphism_theorem",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.isomorphism_theorem",
        "locale": "id-ID",
        "preferred_id": "teorema isomorfisme",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.isomorphism_theorem",
          "english": "isomorphism theorem",
          "first_o014_unit": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "link_status": "o014_new",
          "notes": "Versi kategori abelian dari teorema isomorfisme modul",
          "o013_o014_preferred_id": "teorema isomorfisme",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
      ],
      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
          "unit_id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-026"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.semisimple_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.semisimple_object",
        "locale": "id-ID",
        "preferred_id": "objek semisederhana",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.semisimple_object",
          "english": "semisimple object",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Objek yang merupakan jumlah langsung keluarga objek sederhana",
          "o013_o014_preferred_id": "objek semisederhana",
          "variants": "objek semi-sederhana"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.split_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.split_object",
        "locale": "id-ID",
        "preferred_id": "objek terbelah",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.split_object",
          "english": "split object",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Objek yang semua barisan eksak pendeknya terbelah",
          "o013_o014_preferred_id": "objek terbelah",
          "variants": "objek split"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.semisimple_abelian_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.semisimple_abelian_category",
        "locale": "id-ID",
        "preferred_id": "kategori abelian semisederhana",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.semisimple_abelian_category",
          "english": "semisimple Abelian category",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Kategori yang semua objeknya semisederhana",
          "o013_o014_preferred_id": "kategori abelian semisederhana",
          "variants": "kategori semisimple"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.split_abelian_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.split_abelian_category",
        "locale": "id-ID",
        "preferred_id": "kategori abelian terbelah",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.split_abelian_category",
          "english": "split Abelian category",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Kategori yang semua objeknya terbelah",
          "o013_o014_preferred_id": "kategori abelian terbelah",
          "variants": "kategori split"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.composition_factor",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.composition_factor",
        "locale": "id-ID",
        "preferred_id": "faktor komposisi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.composition_factor",
          "english": "composition factor",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Subkuosien sederhana dalam deret komposisi",
          "o013_o014_preferred_id": "faktor komposisi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.multiplicity",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.multiplicity",
        "locale": "id-ID",
        "preferred_id": "multiplicitas",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.multiplicity",
          "english": "multiplicity",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Banyaknya kemunculan suatu faktor dalam multihimpunan",
          "o013_o014_preferred_id": "multiplicitas",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.division_ring",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.division_ring",
        "locale": "id-ID",
        "preferred_id": "gelanggang pembagian",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.division_ring",
          "english": "division ring",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Gelanggang tempat setiap unsur tak nol invertibel",
          "o013_o014_preferred_id": "gelanggang pembagian",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.schur_lemma",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.schur_lemma",
        "locale": "id-ID",
        "preferred_id": "Lema Schur",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.schur_lemma",
          "english": "Schur lemma",
          "first_o014_unit": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "link_status": "o014_new",
          "notes": "Lema tentang morfisme tak nol antara objek sederhana",
          "o013_o014_preferred_id": "Lema Schur",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.simplicity-and-semisimplicity"
      ],
      "unit_links": [
        {
          "title": "Objek Sederhana dan Semisederhana",
          "unit_id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-027"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.exact_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.exact_functor",
        "locale": "id-ID",
        "preferred_id": "funktor eksak",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.exact_functor",
          "english": "exact functor",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Funktor aditif yang mempertahankan barisan eksak pendek dan barisan eksak.",
          "o013_o014_preferred_id": "funktor eksak",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.left_exact_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.left_exact_functor",
        "locale": "id-ID",
        "preferred_id": "funktor eksak kiri",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.left_exact_functor",
          "english": "left exact functor",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Funktor yang mempertahankan kernel atau limit hingga.",
          "o013_o014_preferred_id": "funktor eksak kiri",
          "variants": "funktor kiri-eksak"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.right_exact_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.right_exact_functor",
        "locale": "id-ID",
        "preferred_id": "funktor eksak kanan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.right_exact_functor",
          "english": "right exact functor",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Funktor yang mempertahankan kokernel atau kolimit hingga.",
          "o013_o014_preferred_id": "funktor eksak kanan",
          "variants": "funktor kanan-eksak"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.faithfully_exact_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.faithfully_exact_functor",
        "locale": "id-ID",
        "preferred_id": "funktor eksak setia",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.faithfully_exact_functor",
          "english": "faithfully exact functor",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Funktor eksak yang juga setia.",
          "o013_o014_preferred_id": "funktor eksak setia",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.enough_injective_objects",
      "kind": "terms",
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        "concept_id": "math.category.enough_injective_objects",
        "locale": "id-ID",
        "preferred_id": "cukup banyak objek injektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.enough_injective_objects",
          "english": "enough injectives",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Setiap objek membenam ke objek injektif.",
          "o013_o014_preferred_id": "cukup banyak objek injektif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.enough_projective_objects",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.enough_projective_objects",
        "locale": "id-ID",
        "preferred_id": "cukup banyak objek projektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.enough_projective_objects",
          "english": "enough projectives",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Setiap objek merupakan kuosien objek projektif.",
          "o013_o014_preferred_id": "cukup banyak objek projektif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.arrow_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.arrow_category",
        "locale": "id-ID",
        "preferred_id": "kategori panah",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.arrow_category",
          "english": "arrow category",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Kategori funktor untuk diagram 0 ke 1.",
          "o013_o014_preferred_id": "kategori panah",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.localization_exactness",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.localization_exactness",
        "locale": "id-ID",
        "preferred_id": "keeksakan lokalisasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.localization_exactness",
          "english": "exactness of localization",
          "first_o014_unit": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "link_status": "o014_new",
          "notes": "Lokalisasi kategori abelian oleh keluarga multiplikatif tetap eksak.",
          "o013_o014_preferred_id": "keeksakan lokalisasi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.exact-functors-injective-projective-objects"
      ],
      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
          "unit_id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-028"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.weak_serre_subcategory",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.weak_serre_subcategory",
        "locale": "id-ID",
        "preferred_id": "subkategori Serre lemah",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.weak_serre_subcategory",
          "english": "weak Serre subcategory",
          "first_o014_unit": "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups",
          "link_status": "o014_new",
          "notes": "Subkategori penuh yang memenuhi kondisi penutupan lima-suku dalam definisi sumber.",
          "o013_o014_preferred_id": "subkategori Serre lemah",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups"
      ],
      "unit_links": [
        {
          "title": "Subkategori Serre dan Grup K0",
          "unit_id": "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-029"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.small_skeleton",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.small_skeleton",
        "locale": "id-ID",
        "preferred_id": "kerangka kecil",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.small_skeleton",
          "english": "small skeleton",
          "first_o014_unit": "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups",
          "link_status": "o014_new",
          "notes": "Kerangka suatu kategori dengan kelas objek berupa himpunan kecil.",
          "o013_o014_preferred_id": "kerangka kecil",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups"
      ],
      "unit_links": [
        {
          "title": "Subkategori Serre dan Grup K0",
          "unit_id": "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-029"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.s_torsion_module",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.s_torsion_module",
        "locale": "id-ID",
        "preferred_id": "modul torsi-S",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.s_torsion_module",
          "english": "S-torsion module",
          "first_o014_unit": "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups",
          "link_status": "o014_new",
          "notes": "Modul yang setiap unsurnya dimatikan oleh suatu unsur dari himpunan multiplikatif S.",
          "o013_o014_preferred_id": "modul torsi-S",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups"
      ],
      "unit_links": [
        {
          "title": "Subkategori Serre dan Grup K0",
          "unit_id": "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-029"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.strong_generator",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.strong_generator",
        "locale": "id-ID",
        "preferred_id": "generator kuat",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.strong_generator",
          "english": "strong generator",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Generator yang mendeteksi kapan monomorfisme merupakan isomorfisme.",
          "o013_o014_preferred_id": "generator kuat",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.injective_cogenerator",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.injective_cogenerator",
        "locale": "id-ID",
        "preferred_id": "kogenerator injektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.injective_cogenerator",
          "english": "injective cogenerator",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Kogenerator yang sekaligus merupakan objek injektif.",
          "o013_o014_preferred_id": "kogenerator injektif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.small_object_argument",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.small_object_argument",
        "locale": "id-ID",
        "preferred_id": "argumen objek kecil",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.small_object_argument",
          "english": "small object argument",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Konstruksi transfinit yang memperluas morfisme secara funktorial.",
          "o013_o014_preferred_id": "argumen objek kecil",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.alpha_small_object_relative_to_i",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.alpha_small_object_relative_to_i",
        "locale": "id-ID",
        "preferred_id": "objek alpha-kecil relatif terhadap I",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.alpha_small_object_relative_to_i",
          "english": "alpha-small object relative to I",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Objek yang Hom-nya mengkomutasi dengan kolimit ordinal terfilter yang morfisme transisinya berada dalam I.",
          "o013_o014_preferred_id": "objek alpha-kecil relatif terhadap I",
          "variants": "objek $\\alpha$-kecil relatif terhadap $I$"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "term_disagreement"
      ],
      "id": "math.set_theory.regular_small_cardinal",
      "kind": "terms",
      "native": {
        "concept_id": "math.set_theory.regular_small_cardinal",
        "locale": "id-ID",
        "preferred_id": "kardinal kecil reguler",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.set_theory.regular_small_cardinal",
          "english": "regular small cardinal",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Kardinal regular yang kecil relatif terhadap semesta Grothendieck terpilih.",
          "o013_o014_preferred_id": "kardinal kecil regular",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.set_theory.transfinite_recursion",
      "kind": "terms",
      "native": {
        "concept_id": "math.set_theory.transfinite_recursion",
        "locale": "id-ID",
        "preferred_id": "rekursi transfinit",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.set_theory.transfinite_recursion",
          "english": "transfinite recursion",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Rekursi sepanjang ordinal penerus dan ordinal limit.",
          "o013_o014_preferred_id": "rekursi transfinit",
          "variants": "rekursi transhingga"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.set_theory.successor_ordinal",
      "kind": "terms",
      "native": {
        "concept_id": "math.set_theory.successor_ordinal",
        "locale": "id-ID",
        "preferred_id": "ordinal penerus",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.set_theory.successor_ordinal",
          "english": "successor ordinal",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Ordinal berbentuk beta tambah satu.",
          "o013_o014_preferred_id": "ordinal penerus",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.set_theory.limit_ordinal",
      "kind": "terms",
      "native": {
        "concept_id": "math.set_theory.limit_ordinal",
        "locale": "id-ID",
        "preferred_id": "ordinal limit",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.set_theory.limit_ordinal",
          "english": "limit ordinal",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Ordinal tak nol yang bukan ordinal penerus.",
          "o013_o014_preferred_id": "ordinal limit",
          "variants": "ordinal batas"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.category.karoubi_envelope",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.karoubi_envelope",
        "locale": "id-ID",
        "preferred_id": "selubung Karoubi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.karoubi_envelope",
          "english": "Karoubi envelope",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Kategori yang diperoleh dengan menambahkan secara formal semua suku jumlah langsung.",
          "o013_o014_preferred_id": "selubung Karoubi",
          "variants": "penyelesaian Karoubi"
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      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "kind": "terms",
      "native": {
        "concept_id": "math.homological.schanuel_lemma",
        "locale": "id-ID",
        "preferred_id": "Lema Schanuel",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.schanuel_lemma",
          "english": "Schanuel lemma",
          "first_o014_unit": "o014.aljabr2.chapter2.grothendieck-categories",
          "link_status": "o014_new",
          "notes": "Lema yang membandingkan kernel dua presentasi projektif dari objek yang sama.",
          "o013_o014_preferred_id": "Lema Schanuel",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter2.grothendieck-categories"
      ],
      "unit_links": [
        {
          "title": "Kategori Grothendieck",
          "unit_id": "o014.aljabr2.chapter2.grothendieck-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-030"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.complex_homotopy",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.complex_homotopy",
        "locale": "id-ID",
        "preferred_id": "homotopi kompleks",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.complex_homotopy",
          "english": "complex homotopy",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Relasi homotopi antara morfisme kompleks; Unit 048 uses the explicit relation noun phrase.",
          "o013_o014_preferred_id": "homotopi kompleks",
          "variants": "homotopi; relasi homotopi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.hom_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.hom_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks Hom",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.hom_complex",
          "english": "Hom complex",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Kompleks internal yang suku dan diferensialnya dibentuk dari Hom antara dua kompleks.",
          "o013_o014_preferred_id": "kompleks Hom",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.total_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.total_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks total",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.total_complex",
          "english": "total complex",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Kompleks yang diperoleh dengan meratakan bikompleks melalui jumlah langsung atau hasil kali langsung.",
          "o013_o014_preferred_id": "kompleks total",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.long_exact_sequence",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.long_exact_sequence",
        "locale": "id-ID",
        "preferred_id": "barisan eksak panjang",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.long_exact_sequence",
          "english": "long exact sequence",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Barisan eksak yang menghubungkan kohomologi atau homologi pada derajat berurutan.",
          "o013_o014_preferred_id": "barisan eksak panjang",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.resolution",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.resolution",
        "locale": "id-ID",
        "preferred_id": "resolusi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.resolution",
          "english": "resolution",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Penggantian objek atau kompleks melalui kuasi-isomorfisme oleh kompleks dengan sifat yang lebih baik.",
          "o013_o014_preferred_id": "resolusi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.truncation_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.truncation_functor",
        "locale": "id-ID",
        "preferred_id": "funktor pemenggalan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.truncation_functor",
          "english": "truncation functor",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Funktor yang memenggal kompleks menurut batas derajat.",
          "o013_o014_preferred_id": "funktor pemenggalan",
          "variants": "funktor trunkasi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.cartan_eilenberg_resolution",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.cartan_eilenberg_resolution",
        "locale": "id-ID",
        "preferred_id": "resolusi Cartan-Eilenberg",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.cartan_eilenberg_resolution",
          "english": "Cartan-Eilenberg resolution",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Resolusi bikompleks yang menyelaraskan resolusi suku dan kohomologi suatu kompleks.",
          "o013_o014_preferred_id": "resolusi Cartan-Eilenberg",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.homological.hyperderived_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.hyperderived_functor",
        "locale": "id-ID",
        "preferred_id": "funktor hiperturunan",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.hyperderived_functor",
          "english": "hyperderived functor",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_provisional",
          "notes": "Versi klasik funktor turunan yang dievaluasi pada kompleks terbatas satu sisi; bentuk Indonesia logis tetapi belum terattestasi kuat.",
          "o013_o014_preferred_id": "funktor hiperturunan",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.effaceable_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.effaceable_functor",
        "locale": "id-ID",
        "preferred_id": "funktor yang dapat dihapus",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.effaceable_functor",
          "english": "effaceable functor",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Funktor yang dapat dinolkan setelah pembenaman objek yang sesuai; bentuk pilihan dikukuhkan oleh definisi formal dalam Unit 043.",
          "o013_o014_preferred_id": "funktor yang dapat dihapus",
          "variants": "funktor terhapuskan"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.coeffaceable_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.coeffaceable_functor",
        "locale": "id-ID",
        "preferred_id": "funktor yang dapat dihapus secara dual",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.coeffaceable_functor",
          "english": "co-effaceable functor",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Dual melalui epimorfisme yang sesuai; bentuk pilihan dikukuhkan oleh definisi formal dalam Unit 043.",
          "o013_o014_preferred_id": "funktor yang dapat dihapus secara dual",
          "variants": "funktor koterhapuskan"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.bifunctor",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.bifunctor",
        "locale": "id-ID",
        "preferred_id": "bifunktor",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.bifunctor",
          "english": "bifunctor",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Funktor dengan dua variabel kategori.",
          "o013_o014_preferred_id": "bifunktor",
          "variants": "funktor dua variabel"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.balanced_bifunctor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.balanced_bifunctor",
        "locale": "id-ID",
        "preferred_id": "bifunktor seimbang",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.balanced_bifunctor",
          "english": "balanced bifunctor",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Bifunktor yang penurunannya terhadap salah satu variabel memberikan hasil yang sama.",
          "o013_o014_preferred_id": "bifunktor seimbang",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.mittag_leffler_condition",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.mittag_leffler_condition",
        "locale": "id-ID",
        "preferred_id": "syarat Mittag-Leffler",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.mittag_leffler_condition",
          "english": "Mittag-Leffler condition",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Syarat kestabilan citra dalam sistem invers yang membantu menjamin lenyapnya lim pangkat satu.",
          "o013_o014_preferred_id": "syarat Mittag-Leffler",
          "variants": "kondisi Mittag-Leffler"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.k_injective_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.k_injective_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks K-injektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.k_injective_complex",
          "english": "K-injective complex",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Kompleks dengan sifat injektivitas homotopis secara keseluruhan.",
          "o013_o014_preferred_id": "kompleks K-injektif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.k_projective_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.k_projective_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks K-projektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.k_projective_complex",
          "english": "K-projective complex",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Kompleks dengan sifat projektivitas homotopis secara keseluruhan.",
          "o013_o014_preferred_id": "kompleks K-projektif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
      ],
      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.mapping_cylinder",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.mapping_cylinder",
        "locale": "id-ID",
        "preferred_id": "silinder pemetaan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.mapping_cylinder",
          "english": "mapping cylinder",
          "first_o014_unit": "o014.aljabr2.chapter3.overview",
          "link_status": "o014_new",
          "notes": "Konstruksi kompleks yang berpasangan dengan kerucut pemetaan.",
          "o013_o014_preferred_id": "silinder pemetaan",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.overview"
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      "unit_links": [
        {
          "title": "Kompleks",
          "unit_id": "o014.aljabr2.chapter3.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-031"
        }
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.graded_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.graded_object",
        "locale": "id-ID",
        "preferred_id": "objek bergradasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.graded_object",
          "english": "graded object",
          "first_o014_unit": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "link_status": "o014_new",
          "notes": "Objek dalam kategori produk berindeks derajat; jangan campurkan pergeseran tanpa tanda T dengan pergeseran kompleks bertanda [n].",
          "o013_o014_preferred_id": "objek bergradasi",
          "variants": "objek berderajat"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.complexes-over-additive-categories"
      ],
      "unit_links": [
        {
          "title": "Kompleks pada Kategori Aditif",
          "unit_id": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-032"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.differential_graded_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.differential_graded_object",
        "locale": "id-ID",
        "preferred_id": "objek diferensial bergradasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.differential_graded_object",
          "english": "differential graded object",
          "first_o014_unit": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "link_status": "o014_new",
          "notes": "Objek bergradasi X dengan diferensial d:X ke TX yang memenuhi (Td)d=0.",
          "o013_o014_preferred_id": "objek diferensial bergradasi",
          "variants": "objek dg"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.complexes-over-additive-categories"
      ],
      "unit_links": [
        {
          "title": "Kompleks pada Kategori Aditif",
          "unit_id": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-032"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.bigraded_object",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.bigraded_object",
        "locale": "id-ID",
        "preferred_id": "objek bergradasi ganda",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.bigraded_object",
          "english": "bigraded object",
          "first_o014_unit": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "link_status": "o014_new",
          "notes": "Kasus objek bergradasi Z pangkat m dengan m=2.",
          "o013_o014_preferred_id": "objek bergradasi ganda",
          "variants": "objek bigradasi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.complexes-over-additive-categories"
      ],
      "unit_links": [
        {
          "title": "Kompleks pada Kategori Aditif",
          "unit_id": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-032"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.complex_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.complex_category",
        "locale": "id-ID",
        "preferred_id": "kategori kompleks",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.complex_category",
          "english": "category of complexes",
          "first_o014_unit": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "link_status": "o014_new",
          "notes": "Kategori C(A) yang objeknya kompleks dan morfismenya morfisme kompleks.",
          "o013_o014_preferred_id": "kategori kompleks",
          "variants": "kategori kompleks-kompleks"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.complexes-over-additive-categories"
      ],
      "unit_links": [
        {
          "title": "Kompleks pada Kategori Aditif",
          "unit_id": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-032"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.concentrated_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.concentrated_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks terkonsentrasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.concentrated_complex",
          "english": "complex concentrated in a degree",
          "first_o014_unit": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "link_status": "o014_new",
          "notes": "Kompleks S[-n] menempatkan S hanya pada derajat n dan nol pada derajat lain.",
          "o013_o014_preferred_id": "kompleks terkonsentrasi",
          "variants": "kompleks yang terkonsentrasi pada suatu derajat"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.complexes-over-additive-categories"
      ],
      "unit_links": [
        {
          "title": "Kompleks pada Kategori Aditif",
          "unit_id": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-032"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.leibniz_rule",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.leibniz_rule",
        "locale": "id-ID",
        "preferred_id": "aturan Leibniz",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.leibniz_rule",
          "english": "Leibniz rule",
          "first_o014_unit": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "link_status": "o014_new",
          "notes": "Aturan tanda untuk diferensial terhadap perkalian homogen dalam kompleks Hom.",
          "o013_o014_preferred_id": "aturan Leibniz",
          "variants": "kaidah Leibniz"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.hom-complex-and-homotopy"
      ],
      "unit_links": [
        {
          "title": "Kompleks Hom dan Homotopi",
          "unit_id": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-033"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.homotopic_morphism",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.homotopic_morphism",
        "locale": "id-ID",
        "preferred_id": "morfisme homotopik",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.homotopic_morphism",
          "english": "homotopic morphisms",
          "first_o014_unit": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "link_status": "o014_new",
          "notes": "Dua morfisme kompleks yang selisihnya merupakan batas dalam kompleks Hom.",
          "o013_o014_preferred_id": "morfisme homotopik",
          "variants": "morfisme yang homotopi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.hom-complex-and-homotopy"
      ],
      "unit_links": [
        {
          "title": "Kompleks Hom dan Homotopi",
          "unit_id": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-033"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.null_homotopic_morphism",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.null_homotopic_morphism",
        "locale": "id-ID",
        "preferred_id": "morfisme homotopik nol",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.null_homotopic_morphism",
          "english": "null-homotopic morphism",
          "first_o014_unit": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "link_status": "o014_new",
          "notes": "Morfisme kompleks yang homotopik dengan morfisme nol.",
          "o013_o014_preferred_id": "morfisme homotopik nol",
          "variants": "morfisme homotopik dengan morfisme nol"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.hom-complex-and-homotopy"
      ],
      "unit_links": [
        {
          "title": "Kompleks Hom dan Homotopi",
          "unit_id": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-033"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.homotopy_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.homotopy_category",
        "locale": "id-ID",
        "preferred_id": "kategori homotopi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.homotopy_category",
          "english": "homotopy category",
          "first_o014_unit": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "link_status": "o014_new",
          "notes": "Kategori K(A) dengan objek kompleks dan morfisme berupa kelas homotopi; bentuk ini juga terattestasi dalam saksi istilah ITB 2020.",
          "o013_o014_preferred_id": "kategori homotopi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.hom-complex-and-homotopy"
      ],
      "unit_links": [
        {
          "title": "Kompleks Hom dan Homotopi",
          "unit_id": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-033"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.homotopy_cokernel",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.homotopy_cokernel",
        "locale": "id-ID",
        "preferred_id": "kokernel homotopi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.homotopy_cokernel",
          "english": "homotopy cokernel",
          "first_o014_unit": "o014.aljabr2.chapter3.mapping-cone",
          "link_status": "o014_new",
          "notes": "Morfisme Y ke Cone(f) yang memfaktorkan morfisme u ketika uf homotopik nol sekaligus membawa data homotopinya.",
          "o013_o014_preferred_id": "kokernel homotopi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.mapping-cone"
      ],
      "unit_links": [
        {
          "title": "Kerucut pemetaan",
          "unit_id": "o014.aljabr2.chapter3.mapping-cone",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-034"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.homotopy_kernel",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.homotopy_kernel",
        "locale": "id-ID",
        "preferred_id": "kernel homotopi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.homotopy_kernel",
          "english": "homotopy kernel",
          "first_o014_unit": "o014.aljabr2.chapter3.mapping-cone",
          "link_status": "o014_new",
          "notes": "Morfisme Cone(f)[-1] ke X yang memfaktorkan morfisme v ketika fv homotopik nol sekaligus membawa data homotopinya.",
          "o013_o014_preferred_id": "kernel homotopi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.mapping-cone"
      ],
      "unit_links": [
        {
          "title": "Kerucut pemetaan",
          "unit_id": "o014.aljabr2.chapter3.mapping-cone",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-034"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.homotopy_coimage",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.homotopy_coimage",
        "locale": "id-ID",
        "preferred_id": "kocitra homotopi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.homotopy_coimage",
          "english": "homotopy coimage",
          "first_o014_unit": "o014.aljabr2.chapter3.mapping-cone",
          "link_status": "o014_new",
          "notes": "Peran silinder pemetaan sebagai analog homotopik kocitra suatu morfisme kompleks.",
          "o013_o014_preferred_id": "kocitra homotopi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.mapping-cone"
      ],
      "unit_links": [
        {
          "title": "Kerucut pemetaan",
          "unit_id": "o014.aljabr2.chapter3.mapping-cone",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-034"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.koszul_sign_rule",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.koszul_sign_rule",
        "locale": "id-ID",
        "preferred_id": "aturan tanda Koszul",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.koszul_sign_rule",
          "english": "Koszul sign rule",
          "first_o014_unit": "o014.aljabr2.chapter3.double-complexes",
          "link_status": "o014_new",
          "notes": "Aturan tanda berderajat yang menghasilkan faktor Koszul seperti (-1)^{pq}; no exact Indonesian attestation was located in the bounded Unit 036 field search.",
          "o013_o014_preferred_id": "aturan tanda Koszul",
          "variants": "kaidah tanda Koszul"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
      ],
      "unit_links": [
        {
          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.k_fold_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.k_fold_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks lipat-k",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.k_fold_complex",
          "english": "k-fold complex",
          "first_o014_unit": "o014.aljabr2.chapter3.double-complexes",
          "link_status": "o014_provisional",
          "notes": "Kompleks dengan k arah diferensial yang saling berkomutasi.",
          "o013_o014_preferred_id": "kompleks lipat-k",
          "variants": "kompleks k-rangkap"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
      ],
      "unit_links": [
        {
          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.hom_bicomplex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.hom_bicomplex",
        "locale": "id-ID",
        "preferred_id": "bikompleks Hom",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.hom_bicomplex",
          "english": "Hom bicomplex",
          "first_o014_unit": "o014.aljabr2.chapter3.double-complexes",
          "link_status": "o014_new",
          "notes": "Bikompleks yang dibentuk dari Hom antara dua kompleks; no exact Indonesian field attestation was located and the transparent form remains provisional.",
          "o013_o014_preferred_id": "bikompleks Hom",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
      ],
      "unit_links": [
        {
          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.bicomplex_homotopy",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.bicomplex_homotopy",
        "locale": "id-ID",
        "preferred_id": "homotopi bikompleks",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bicomplex_homotopy",
          "english": "bicomplex homotopy",
          "first_o014_unit": "o014.aljabr2.chapter3.double-complexes",
          "link_status": "o014_new",
          "notes": "Homotopi dua-arah antara morfisme bikompleks; homotopi is strongly attested by the ITB 2020 same-field witness while the compound is not directly attested.",
          "o013_o014_preferred_id": "homotopi bikompleks",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
      ],
      "unit_links": [
        {
          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.rotation_axiom",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.rotation_axiom",
        "locale": "id-ID",
        "preferred_id": "aksioma rotasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.rotation_axiom",
          "english": "rotation axiom",
          "first_o014_unit": "o014.aljabr2.chapter3.mapping-cone-and-long-exact-sequences",
          "link_status": "o014_new",
          "notes": "Aksioma rotasi untuk kategori bertriangulasi; penanda (TR3) mengikuti penomoran sumber.",
          "o013_o014_preferred_id": "aksioma rotasi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.mapping-cone-and-long-exact-sequences"
      ],
      "unit_links": [
        {
          "title": "Kerucut pemetaan: barisan eksak panjang",
          "unit_id": "o014.aljabr2.chapter3.mapping-cone-and-long-exact-sequences",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-038"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.tensor_power",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.tensor_power",
        "locale": "id-ID",
        "preferred_id": "pangkat tensor",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.tensor_power",
          "english": "tensor power",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "Use pangkat tensor ke-n for $M^{\\otimes n}$ and retain $M^{\\otimes 0}:=\\Bbbk$.",
          "o013_o014_preferred_id": "pangkat tensor",
          "variants": "hasil kali tensor berulang; hasil kali tensor lipat-n"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.bar_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.bar_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks bar",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bar_complex",
          "english": "bar complex",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "Use bar unchanged and distinguish this from the existing konstruksi bar entry.",
          "o013_o014_preferred_id": "kompleks bar",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.augmented_bar_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.augmented_bar_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks bar teraugmentasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.augmented_bar_complex",
          "english": "augmented bar complex",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "For $\\mathsf{B}'R$; it is $\\Bbbk$-split contractible and is not automatically an $R^e$-projective resolution.",
          "o013_o014_preferred_id": "kompleks bar teraugmentasi",
          "variants": "kompleks bar beraugmentasi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.augmentation_morphism",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.augmentation_morphism",
        "locale": "id-ID",
        "preferred_id": "homomorfisme augmentasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.augmentation_morphism",
          "english": "augmentation homomorphism",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "For $b_0:R\\otimes R\\to R$; this chain augmentation is multiplication and does not define an augmentation ideal.",
          "o013_o014_preferred_id": "homomorfisme augmentasi",
          "variants": "morfisme augmentasi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.comonad",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.comonad",
        "locale": "id-ID",
        "preferred_id": "komonad",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.comonad",
          "english": "comonad",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "Aligned with the existing monad terminology.",
          "o013_o014_preferred_id": "komonad",
          "variants": "komonada"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.hochschild_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.hochschild_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks Hochschild",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.hochschild_complex",
          "english": "Hochschild complex",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "Umbrella entry for $C_\\bullet(R,M)$ and $C^\\bullet(R,M)$.",
          "o013_o014_preferred_id": "kompleks Hochschild",
          "variants": "kompleks rantai Hochschild; kompleks kokrantai Hochschild"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.relative_tor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.relative_tor",
        "locale": "id-ID",
        "preferred_id": "Tor relatif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.relative_tor",
          "english": "relative Tor",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "Forward reference; preserve the symbol Tor.",
          "o013_o014_preferred_id": "Tor relatif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.relative_ext",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.relative_ext",
        "locale": "id-ID",
        "preferred_id": "Ext relatif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.relative_ext",
          "english": "relative Ext",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "Forward reference; preserve the symbol Ext.",
          "o013_o014_preferred_id": "Ext relatif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.center",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.center",
        "locale": "id-ID",
        "preferred_id": "pusat",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.center",
          "english": "center",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "For elements of an $(R,R)$-bimodule commuting with every $r\\in R$; this is the ring center when $M=R$.",
          "o013_o014_preferred_id": "pusat",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.cocenter",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.cocenter",
        "locale": "id-ID",
        "preferred_id": "kopusat",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.cocenter",
          "english": "cocenter",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "For $M/[M,R]$ and especially $R/[R,R]$; retain the English gloss at first use.",
          "o013_o014_preferred_id": "kopusat",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.kahler_differentials",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.kahler_differentials",
        "locale": "id-ID",
        "preferred_id": "diferensial Kähler",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.kahler_differentials",
          "english": "Kähler differentials",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "Use modul diferensial Kähler for the module $\\Omega_{R\\mid\\Bbbk}$.",
          "o013_o014_preferred_id": "diferensial Kähler",
          "variants": "modul diferensial Kähler; bentuk diferensial Kähler"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.universal_derivation",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.universal_derivation",
        "locale": "id-ID",
        "preferred_id": "derivasi universal",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.universal_derivation",
          "english": "universal derivation",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "For $r\\mapsto \\mathrm dr$ and the universal property $\\Hom_R(\\Omega_{R\\mid\\Bbbk},M)\\simeq\\Der_\\Bbbk(R,M)$.",
          "o013_o014_preferred_id": "derivasi universal",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.cyclic_bicomplex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.cyclic_bicomplex",
        "locale": "id-ID",
        "preferred_id": "bikompleks siklik",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.cyclic_bicomplex",
          "english": "cyclic double complex",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "For $\\mathrm{CC}(R)$; use bikompleks kokrantai siklik for the dual cochain version $\\mathrm{CC}'(R)$.",
          "o013_o014_preferred_id": "bikompleks siklik",
          "variants": "kompleks ganda siklik"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.homological.brutal_truncation",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.brutal_truncation",
        "locale": "id-ID",
        "preferred_id": "pemenggalan kasar",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.brutal_truncation",
          "english": "brutal truncation",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_provisional",
          "notes": "Retain the English gloss at first use and let the displayed sigma formula control the meaning.",
          "o013_o014_preferred_id": "pemenggalan kasar",
          "variants": "pemenggalan brutal; pemenggalan naif; trunkasi brutal"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.cyclic_homology",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.cyclic_homology",
        "locale": "id-ID",
        "preferred_id": "homologi siklik",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.cyclic_homology",
          "english": "cyclic homology",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "homologi siklik",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.periodic_cyclic_homology",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.periodic_cyclic_homology",
        "locale": "id-ID",
        "preferred_id": "homologi siklik periodik",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.periodic_cyclic_homology",
          "english": "periodic cyclic homology",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "",
          "o013_o014_preferred_id": "homologi siklik periodik",
          "variants": "homologi siklik berkala"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.connes_periodicity_operator",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.connes_periodicity_operator",
        "locale": "id-ID",
        "preferred_id": "operator periodisitas Connes",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.connes_periodicity_operator",
          "english": "Connes periodicity operator",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "link_status": "o014_new",
          "notes": "The homological operator has degree $-2$ and the cohomological operator has degree $+2$.",
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          "variants": "operator periodik Connes"
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      },
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        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
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      "related_native": {
        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
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          "o013_o014_preferred_id": "kohomologi siklik",
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      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
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      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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        "concept_id": "math.homological.periodic_cyclic_cohomology",
        "locale": "id-ID",
        "preferred_id": "kohomologi siklik periodik",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.periodic_cyclic_cohomology",
          "english": "periodic cyclic cohomology",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
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          "notes": "",
          "o013_o014_preferred_id": "kohomologi siklik periodik",
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        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
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        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
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    {
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        "concept_id": "math.algebra.linear_dual",
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        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
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          "notes": "For the correction $R^\\vee:=\\Hom_\\Bbbk(R,\\Bbbk)$; use modul dual when emphasizing that $\\Bbbk$ need not be a field.",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bounded_complex",
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          "first_o014_unit": "o014.aljabr2.chapter3.truncation-functors",
          "link_status": "o014_new",
          "notes": "Termwise zero for $|n|\\gg0$; do not confuse this with cohomology vanishing outside a bounded range.",
          "o013_o014_preferred_id": "kompleks terbatas",
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      "unit_ids": [
        "o014.aljabr2.chapter3.truncation-functors"
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      "unit_links": [
        {
          "title": "Funktor pemenggalan",
          "unit_id": "o014.aljabr2.chapter3.truncation-functors",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-040"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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        "concept_id": "math.homological.bounded_below_complex",
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        "preferred_id": "kompleks terbatas bawah",
        "source_course_ids": "O014",
        "status": "active"
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bounded_below_complex",
          "english": "bounded-below complex",
          "first_o014_unit": "o014.aljabr2.chapter3.truncation-functors",
          "link_status": "o014_new",
          "notes": "For $X^n=0$ when $n\\ll0$; corresponds to $\\cate C^+(\\mathcal A)$.",
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          "variants": "kompleks terbatas di bawah; kompleks berbatas bawah"
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      },
      "unit_ids": [
        "o014.aljabr2.chapter3.truncation-functors"
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      "unit_links": [
        {
          "title": "Funktor pemenggalan",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-040"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "kind": "terms",
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        "concept_id": "math.homological.bounded_above_complex",
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        "preferred_id": "kompleks terbatas atas",
        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bounded_above_complex",
          "english": "bounded-above complex",
          "first_o014_unit": "o014.aljabr2.chapter3.truncation-functors",
          "link_status": "o014_new",
          "notes": "For $X^n=0$ when $n\\gg0$; corresponds to $\\cate C^-(\\mathcal A)$.",
          "o013_o014_preferred_id": "kompleks terbatas atas",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter3.truncation-functors"
      ],
      "unit_links": [
        {
          "title": "Funktor pemenggalan",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-040"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "native": {
        "concept_id": "math.homological.diagonally_finite_bicomplex",
        "locale": "id-ID",
        "preferred_id": "bikompleks berhingga pada setiap diagonal",
        "source_course_ids": "O014",
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      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.diagonally_finite_bicomplex",
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          "first_o014_unit": "o014.aljabr2.chapter3.double-complex-cohomology",
          "link_status": "o014_new",
          "notes": "Every set of nonzero components on a fixed diagonal $p+q=n$ is finite; the support need not be globally finite.",
          "o013_o014_preferred_id": "bikompleks berhingga pada setiap diagonal",
          "variants": "bikompleks berhingga secara diagonal"
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      "unit_ids": [
        "o014.aljabr2.chapter3.double-complex-cohomology"
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      "unit_links": [
        {
          "title": "Kohomologi bikompleks",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-041"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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      "id": "math.homological.row_exact_bicomplex",
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        "concept_id": "math.homological.row_exact_bicomplex",
        "locale": "id-ID",
        "preferred_id": "bikompleks eksak pada baris",
        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.chapter3.double-complex-cohomology",
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          "notes": "Each horizontal complex $(X^{\\bullet,q},d_h)$ is exact.",
          "o013_o014_preferred_id": "bikompleks eksak pada baris",
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      "unit_ids": [
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        {
          "title": "Kohomologi bikompleks",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-041"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "native": {
        "concept_id": "math.homological.column_exact_bicomplex",
        "locale": "id-ID",
        "preferred_id": "bikompleks eksak pada kolom",
        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
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          "first_o014_unit": "o014.aljabr2.chapter3.double-complex-cohomology",
          "link_status": "o014_new",
          "notes": "Each vertical complex $(X^{p,\\bullet},d_v)$ is exact.",
          "o013_o014_preferred_id": "bikompleks eksak pada kolom",
          "variants": "eksak kolom"
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      },
      "unit_ids": [
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        {
          "title": "Kohomologi bikompleks",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked"
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      "kind": "terms",
      "native": {
        "concept_id": "math.homological.complex_of_injective_objects",
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        "preferred_id": "kompleks yang terdiri atas objek-objek injektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.complex_of_injective_objects",
          "english": "complex of injective objects",
          "first_o014_unit": "o014.aljabr2.chapter3.resolutions",
          "link_status": "o014_new",
          "notes": "Termwise condition in the underlying Abelian category; do not shorten to kompleks injektif because that can suggest an injective object of the complex category or a K-injective complex.",
          "o013_o014_preferred_id": "kompleks yang terdiri atas objek-objek injektif",
          "variants": "kompleks yang tersusun atas objek-objek injektif; kompleks objek injektif"
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      },
      "unit_ids": [
        "o014.aljabr2.chapter3.resolutions"
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      "unit_links": [
        {
          "title": "Resolusi",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "kind": "terms",
      "native": {
        "concept_id": "math.homological.complex_of_projective_objects",
        "locale": "id-ID",
        "preferred_id": "kompleks yang terdiri atas objek-objek projektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.complex_of_projective_objects",
          "english": "complex of projective objects",
          "first_o014_unit": "o014.aljabr2.chapter3.resolutions",
          "link_status": "o014_new",
          "notes": "Termwise condition in the underlying Abelian category; do not shorten to kompleks projektif because that can suggest a projective object of the complex category or a K-projective complex.",
          "o013_o014_preferred_id": "kompleks yang terdiri atas objek-objek projektif",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter3.resolutions"
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      "unit_links": [
        {
          "title": "Resolusi",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
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        "concept_id": "math.homological.horseshoe_lemma",
        "locale": "id-ID",
        "preferred_id": "Lema Tapal Kuda",
        "source_course_ids": "O014",
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          "notes": "Use the English gloss at first visible occurrence and the Indonesian short form thereafter.",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "notes": "Membedakan konstruksi klasik pada objek dari funktor hiperturunan pada kompleks.",
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      "unit_ids": [
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      "unit_links": [
        {
          "title": "Funktor turunan klasik",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
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      "kind": "terms",
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        "source_course_ids": "O014",
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          "first_o014_unit": "o014.aljabr2.chapter3.classical-derived-functors",
          "link_status": "o014_new",
          "notes": "Untuk $\\mathrm{R}^nF$; bentuk khusus dari konsep payung funktor turunan.",
          "o013_o014_preferred_id": "funktor turunan kanan",
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      "unit_ids": [
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      "unit_links": [
        {
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "related_native": {
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          "first_o014_unit": "o014.aljabr2.chapter3.classical-derived-functors",
          "link_status": "o014_new",
          "notes": "Untuk $\\mathrm{L}_nF$; dual dari funktor turunan kanan.",
          "o013_o014_preferred_id": "funktor turunan kiri",
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      },
      "unit_ids": [
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      "unit_links": [
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          "title": "Funktor turunan klasik",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-043"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
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      "kind": "terms",
      "native": {
        "concept_id": "math.homological.higher_derived_functor",
        "locale": "id-ID",
        "preferred_id": "funktor turunan tingkat tinggi",
        "source_course_ids": "O014",
        "status": "active"
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.higher_derived_functor",
          "english": "higher derived functor",
          "first_o014_unit": "o014.aljabr2.chapter3.classical-derived-functors",
          "link_status": "o014_new",
          "notes": "Untuk $\\mathrm{R}^nF$ atau $\\mathrm{L}_nF$ dengan $n\\geq1$.",
          "o013_o014_preferred_id": "funktor turunan tingkat tinggi",
          "variants": "funktor turunan derajat positif"
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      },
      "unit_ids": [
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      "unit_links": [
        {
          "title": "Funktor turunan klasik",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-043"
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      "unit_ids": [
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        {
          "title": "Funktor turunan klasik",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "id": "math.homological.homological_delta_functor",
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          "notes": "Subtipe homologis yang dual dari funktor-δ kohomologis.",
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      "unit_ids": [
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        {
          "title": "Funktor turunan klasik",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "id": "math.homological.f_acyclic_object",
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        "concept_id": "math.homological.f_acyclic_object",
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      "unit_ids": [
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        {
          "title": "Funktor turunan klasik",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "concept_id": "math.homological.dimension_shifting",
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        {
          "title": "Funktor turunan klasik",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        {
          "title": "Funktor turunan klasik",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        {
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "title": "Contoh: lim^1",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "id": "math.category.countable_product",
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          "notes": "Produk yang diindeks oleh Z_{\\geq 0}; dibedakan dari produk hingga.",
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        }
      },
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        {
          "title": "Contoh: lim^1",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "notes": "Koproduk yang diindeks oleh Z_{\\geq 0}; pada kategori modul berupa jumlah langsung terhitung.",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "notes": "Bifunktor turunan kiri dari hasil kali tensor; pertahankan simbol Tor dan lokalkan functor menjadi funktor.",
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      },
      "unit_ids": [
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          "title": "Contoh: Ext dan Tor",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      },
      "unit_ids": [
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          "title": "Contoh: Ext dan Tor",
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      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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          "notes": "Barisan eksak pendek kanonik yang menghubungkan homologi produk tensor dengan suku Tor.",
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      "unit_links": [
        {
          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.homological.enough_k_projective_complexes",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.enough_k_projective_complexes",
        "locale": "id-ID",
        "preferred_id": "cukup banyak kompleks K-projektif",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.enough_k_projective_complexes",
          "english": "enough K-projectives",
          "first_o014_unit": "o014.aljabr2.chapter3.k-injectives",
          "link_status": "o014_new",
          "notes": "Setiap kompleks menerima kuasi-isomorfisme dari kompleks K-projektif; jangan samakan dengan cukup banyak objek projektif.",
          "o013_o014_preferred_id": "cukup banyak kompleks K-projektif",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
      ],
      "unit_links": [
        {
          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.split_exact_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.split_exact_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks eksak terbelah",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.split_exact_complex",
          "english": "split exact complex",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises",
          "link_status": "o014_new",
          "notes": "Kompleks yang eksak melalui pemisahan pada tiap derajat; bentuk indeks ringkasnya ialah eksak terbelah.",
          "o013_o014_preferred_id": "kompleks eksak terbelah",
          "variants": "kompleks eksak split"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises"
      ],
      "unit_links": [
        {
          "title": "Latihan",
          "unit_id": "o014.aljabr2.chapter3.exercises",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-047"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.reduced_bar_complex",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.reduced_bar_complex",
        "locale": "id-ID",
        "preferred_id": "kompleks bar tereduksi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.reduced_bar_complex",
          "english": "reduced bar complex",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises",
          "link_status": "o014_new",
          "notes": "Kompleks bar setelah bagian satuan direduksi; dipakai untuk perhitungan homologi Hochschild.",
          "o013_o014_preferred_id": "kompleks bar tereduksi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises"
      ],
      "unit_links": [
        {
          "title": "Latihan",
          "unit_id": "o014.aljabr2.chapter3.exercises",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-047"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.algebra.square_zero_extension",
      "kind": "terms",
      "native": {
        "concept_id": "math.algebra.square_zero_extension",
        "locale": "id-ID",
        "preferred_id": "perluasan kuadrat-nol",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.algebra.square_zero_extension",
          "english": "square-zero extension",
          "first_o014_unit": "o014.aljabr2.chapter3.exercises",
          "link_status": "o014_new",
          "notes": "Perluasan gelanggang dengan ideal yang kuadratnya nol.",
          "o013_o014_preferred_id": "perluasan kuadrat-nol",
          "variants": "perluasan berkuadrat nol"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises"
      ],
      "unit_links": [
        {
          "title": "Latihan",
          "unit_id": "o014.aljabr2.chapter3.exercises",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-047"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.autoequivalence",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.autoequivalence",
        "locale": "id-ID",
        "preferred_id": "autoekuivalensi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.autoequivalence",
          "english": "autoequivalence",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Generic concept first used in the phrase autoekuivalensi pergeseran.",
          "o013_o014_preferred_id": "autoekuivalensi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.cohomological_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.cohomological_functor",
        "locale": "id-ID",
        "preferred_id": "funktor kohomologis",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.cohomological_functor",
          "english": "cohomological functor",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Distinct from the already registered cohomological delta-functor.",
          "o013_o014_preferred_id": "funktor kohomologis",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.verdier_localization",
      "kind": "terms",
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        "concept_id": "math.category.verdier_localization",
        "locale": "id-ID",
        "preferred_id": "lokalisasi Verdier",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.verdier_localization",
          "english": "Verdier localization",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Triangulated-category localization associated with Verdier.",
          "o013_o014_preferred_id": "lokalisasi Verdier",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.triangulated_subcategory",
      "kind": "terms",
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        "concept_id": "math.homological.triangulated_subcategory",
        "locale": "id-ID",
        "preferred_id": "subkategori bertriangulasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.triangulated_subcategory",
          "english": "triangulated subcategory",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_provisional",
          "notes": "Coordinate with the provisional triangulated-category form.",
          "o013_o014_preferred_id": "subkategori bertriangulasi",
          "variants": "subkategori triangulasi; subkategori tersegitigakan"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.bounded_below_derived_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.bounded_below_derived_category",
        "locale": "id-ID",
        "preferred_id": "kategori turunan terbatas bawah",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bounded_below_derived_category",
          "english": "bounded-below derived category",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "The D-plus derived category.",
          "o013_o014_preferred_id": "kategori turunan terbatas bawah",
          "variants": "kategori turunan berbatas bawah"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.bounded_above_derived_category",
      "kind": "terms",
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        "concept_id": "math.homological.bounded_above_derived_category",
        "locale": "id-ID",
        "preferred_id": "kategori turunan terbatas atas",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bounded_above_derived_category",
          "english": "bounded-above derived category",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
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          "notes": "The D-minus derived category.",
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          "variants": "kategori turunan berbatas atas"
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      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.bounded_derived_category",
      "kind": "terms",
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        "concept_id": "math.homological.bounded_derived_category",
        "locale": "id-ID",
        "preferred_id": "kategori turunan terbatas",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.bounded_derived_category",
          "english": "bounded derived category",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "The bounded derived category D-b.",
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      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.unbounded_derived_category",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.unbounded_derived_category",
        "locale": "id-ID",
        "preferred_id": "kategori turunan tak terbatas",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.unbounded_derived_category",
          "english": "unbounded derived category",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "The unrestricted derived category.",
          "o013_o014_preferred_id": "kategori turunan tak terbatas",
          "variants": "kategori turunan tanpa batas"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.homological.derived_functor_amplitude",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.derived_functor_amplitude",
        "locale": "id-ID",
        "preferred_id": "amplitudo funktor turunan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.derived_functor_amplitude",
          "english": "amplitude of a derived functor",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Cohomological displacement range of a derived functor.",
          "o013_o014_preferred_id": "amplitudo funktor turunan",
          "variants": "amplitudo turunan"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.homological.derived_functor_dimension",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.derived_functor_dimension",
        "locale": "id-ID",
        "preferred_id": "dimensi funktor turunan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.derived_functor_dimension",
          "english": "dimension of a derived functor",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Dimension determined from derived-functor amplitude.",
          "o013_o014_preferred_id": "dimensi funktor turunan",
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        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.homological.grothendieck_spectral_sequence",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.grothendieck_spectral_sequence",
        "locale": "id-ID",
        "preferred_id": "barisan spektral Grothendieck",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.grothendieck_spectral_sequence",
          "english": "Grothendieck spectral sequence",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Specific spectral sequence associated with composition of derived functors.",
          "o013_o014_preferred_id": "barisan spektral Grothendieck",
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        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
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      "id": "math.homological.derived_hom_functor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.derived_hom_functor",
        "locale": "id-ID",
        "preferred_id": "funktor RHom",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.derived_hom_functor",
          "english": "derived Hom functor",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Derived-category version of Hom and Ext.",
          "o013_o014_preferred_id": "funktor RHom",
          "variants": "Hom turunan; RHom"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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          "title": "Kategori Bertriangulasi dan Kategori Turunan",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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      "id": "math.homological.derived_bifunctor_theory",
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        "concept_id": "math.homological.derived_bifunctor_theory",
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        "preferred_id": "teori bifunktor turunan",
        "source_course_ids": "O014",
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.derived_bifunctor_theory",
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          "notes": "Theory required for derived functors in two variables.",
          "o013_o014_preferred_id": "teori bifunktor turunan",
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      },
      "unit_ids": [
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          "title": "Kategori Bertriangulasi dan Kategori Turunan",
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    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.derived_inverse_limit_functor",
      "kind": "terms",
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        "concept_id": "math.homological.derived_inverse_limit_functor",
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        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.derived_inverse_limit_functor",
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          "first_o014_unit": "o014.aljabr2.chapter4.overview",
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          "notes": "Total right-derived inverse-limit functor; distinct from the generic inverse limit.",
          "o013_o014_preferred_id": "funktor Rlim",
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        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homotopy.homotopy_limit",
      "kind": "terms",
      "native": {
        "concept_id": "math.homotopy.homotopy_limit",
        "locale": "id-ID",
        "preferred_id": "limit homotopi",
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        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homotopy.homotopy_limit",
          "english": "homotopy limit",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Homotopical replacement underlying the description of Rlim.",
          "o013_o014_preferred_id": "limit homotopi",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.derived_tensor_product",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.derived_tensor_product",
        "locale": "id-ID",
        "preferred_id": "hasil kali tensor turunan",
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        "status": "active"
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      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.derived_tensor_product",
          "english": "derived tensor product",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
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          "notes": "Derived-category version of the tensor product.",
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          "variants": "produk tensor turunan; otimesL"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.triangulated_bifunctor",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.triangulated_bifunctor",
        "locale": "id-ID",
        "preferred_id": "bifunktor bertriangulasi",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.triangulated_bifunctor",
          "english": "triangulated bifunctor",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_provisional",
          "notes": "Coordinate with the provisional triangulated-category form.",
          "o013_o014_preferred_id": "bifunktor bertriangulasi",
          "variants": "bifunktor triangulasi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.associativity_constraint",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.associativity_constraint",
        "locale": "id-ID",
        "preferred_id": "kendala asosiativitas",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.associativity_constraint",
          "english": "associativity constraint",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Coherence constraint for the derived tensor product.",
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          "variants": "kendala asosiatif"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.derived_tensor_hom_adjunction",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.derived_tensor_hom_adjunction",
        "locale": "id-ID",
        "preferred_id": "adjungsi hasil kali tensor turunan-RHom",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.derived_tensor_hom_adjunction",
          "english": "derived tensor-Hom adjunction",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_provisional",
          "notes": "Derived adjunction relating tensor and RHom.",
          "o013_o014_preferred_id": "adjungsi hasil kali tensor turunan-RHom",
          "variants": "keadjungan versi RHom; adjungsi RHom-otimesL"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.k_flat_resolution",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.k_flat_resolution",
        "locale": "id-ID",
        "preferred_id": "resolusi K-datar",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.k_flat_resolution",
          "english": "K-flat resolution",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "Resolution by a K-flat complex.",
          "o013_o014_preferred_id": "resolusi K-datar",
          "variants": ""
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.effaceability",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.effaceability",
        "locale": "id-ID",
        "preferred_id": "keterhapusan",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.effaceability",
          "english": "effaceability",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
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          "notes": "Nominal property corresponding to an effaceable functor.",
          "o013_o014_preferred_id": "keterhapusan",
          "variants": "sifat keterhapusan"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.n_extension",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.n_extension",
        "locale": "id-ID",
        "preferred_id": "ekstensi-n",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.n_extension",
          "english": "n-extension",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
          "link_status": "o014_new",
          "notes": "An n-fold extension used in Yoneda's description of Ext.",
          "o013_o014_preferred_id": "ekstensi-n",
          "variants": "ekstensi n"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.yoneda_ext_theorem",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.yoneda_ext_theorem",
        "locale": "id-ID",
        "preferred_id": "Teorema Yoneda",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.yoneda_ext_theorem",
          "english": "Yoneda theorem for Ext and n-extensions",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
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          "notes": "The theorem identifying Ext classes with equivalence classes of n-extensions.",
          "o013_o014_preferred_id": "Teorema Yoneda",
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        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.unbounded_derived_functor",
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        "concept_id": "math.homological.unbounded_derived_functor",
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        "preferred_id": "funktor turunan tak terbatas",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.unbounded_derived_functor",
          "english": "unbounded derived functor",
          "first_o014_unit": "o014.aljabr2.chapter4.overview",
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          "notes": "Derived functor defined on unbounded derived categories.",
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          "variants": "funktor turunan tanpa batas"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
      ],
      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked",
        "provisional"
      ],
      "id": "math.category.category_with_translation",
      "kind": "terms",
      "native": {
        "concept_id": "math.category.category_with_translation",
        "locale": "id-ID",
        "preferred_id": "kategori dengan pergeseran",
        "source_course_ids": "O014",
        "status": "provisional"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.category_with_translation",
          "english": "category with translation",
          "first_o014_unit": "o014.aljabr2.chapter4.triangulated-category-definition",
          "link_status": "o014_provisional",
          "notes": "Use pergeseran consistently with the established shift terminology; translasi remains a search variant.",
          "o013_o014_preferred_id": "kategori dengan pergeseran",
          "variants": "kategori dengan translasi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.triangulated-category-definition"
      ],
      "unit_links": [
        {
          "title": "Definisi Kategori Bertriangulasi",
          "unit_id": "o014.aljabr2.chapter4.triangulated-category-definition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-049"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.translation_functor",
      "kind": "terms",
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        "concept_id": "math.category.translation_functor",
        "locale": "id-ID",
        "preferred_id": "funktor pergeseran",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.translation_functor",
          "english": "translation functor / shift functor",
          "first_o014_unit": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "link_status": "o014_new",
          "notes": "The same preferred form covers the source terms translation functor and shift functor when T is the category equivalence.",
          "o013_o014_preferred_id": "funktor pergeseran",
          "variants": "funktor translasi"
        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter3.complexes-over-additive-categories"
      ],
      "unit_links": [
        {
          "title": "Kompleks pada Kategori Aditif",
          "unit_id": "o014.aljabr2.chapter3.complexes-over-additive-categories",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-032"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.category.morphism_with_degree",
      "kind": "terms",
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        "concept_id": "math.category.morphism_with_degree",
        "locale": "id-ID",
        "preferred_id": "morfisme berderajat",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.category.morphism_with_degree",
          "english": "morphism with degree",
          "first_o014_unit": "o014.aljabr2.chapter4.triangulated-category-definition",
          "link_status": "o014_new",
          "notes": "Keep distinct from objek bergradasi; the degree may be an integer or a multi-index.",
          "o013_o014_preferred_id": "morfisme berderajat",
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        }
      },
      "unit_ids": [
        "o014.aljabr2.chapter4.triangulated-category-definition"
      ],
      "unit_links": [
        {
          "title": "Definisi Kategori Bertriangulasi",
          "unit_id": "o014.aljabr2.chapter4.triangulated-category-definition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-049"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
      "flags": [
        "canon_not_independently_checked"
      ],
      "id": "math.homological.triangle",
      "kind": "terms",
      "native": {
        "concept_id": "math.homological.triangle",
        "locale": "id-ID",
        "preferred_id": "segitiga",
        "source_course_ids": "O014",
        "status": "active"
      },
      "related_native": {
        "terminology_control": {
          "concept_id": "math.homological.triangle",
          "english": "triangle",
          "first_o014_unit": "o014.aljabr2.chapter4.triangulated-category-definition",
          "link_status": "o014_new",
          "notes": "A composable X-to-Y-to-Z-to-TX sequence in a category with translation; distinguished status is separate.",
          "o013_o014_preferred_id": "segitiga",
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        }
      },
      "unit_ids": [
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      ],
      "unit_links": [
        {
          "title": "Definisi Kategori Bertriangulasi",
          "unit_id": "o014.aljabr2.chapter4.triangulated-category-definition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-049"
        }
      ]
    },
    {
      "discovery_scope": "recorded_first_introduction_not_all_occurrences",
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        "canon_not_independently_checked",
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      "id": "math.homological.pretriangulated_category",
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        "concept_id": "math.homological.pretriangulated_category",
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        "source_course_ids": "O014",
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        "terminology_control": {
          "concept_id": "math.homological.pretriangulated_category",
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          "notes": "Transparent parallel to kategori bertriangulasi; retain pratriangulasi as a search variant pending broader field evidence.",
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      },
      "unit_ids": [
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        {
          "title": "Definisi Kategori Bertriangulasi",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-049"
        }
      ]
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    {
      "discovery_scope": "exact_target_file",
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      "id": "O014-C001",
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        "classification": "mathematical_precision",
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        "evidence": "Charles A. Weibel, An Introduction to Homological Algebra, Chapter 9 (author-hosted MIT copy), https://math.mit.edu/~hrm/palestine/weibel/09-hochschild_and_cyclic_homology.pdf",
        "rationale": "For an associative algebra R with coefficients in the regular bimodule R, HH^1(R,R)=Der(R)/InnDer(R); the source sentence omits the quotient by inner derivations.",
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        "target_lines": "84-92",
        "target_path": "source/id-ID/prelude-unit-002.tex"
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        {
          "title": "Sejarah Singkat Homologi",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-prelude-unit-002"
        }
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      "discovery_scope": "exact_target_file",
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      "id": "O014-C002",
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        "source_line": "1255",
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        "o014.aljabr2.chapter1.gabriel-zisman-localization"
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      "unit_links": [
        {
          "title": "Lokalisasi Gabriel--Zisman",
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        "source_line": "1493",
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        "o014.aljabr2.chapter1.gabriel-zisman-localization"
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      "unit_links": [
        {
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      "discovery_scope": "exact_target_file",
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        "classification": "mathematical_typing_typo",
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        "source_line": "1599",
        "source_path": "chapter1.tex",
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      "unit_ids": [
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        {
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    {
      "discovery_scope": "exact_target_file",
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        "source_line": "1747",
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        "target_claim": "The target tests Hom_E(e,e') and discloses the corrected category subscript",
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      "unit_ids": [
        "o014.aljabr2.chapter1.adjoint-functor-theorem"
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        {
          "title": "Teorema Funktor Adjoin",
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      "discovery_scope": "exact_target_file",
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        "source_line": "648",
        "source_path": "chapter2.tex",
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        "target_claim": "The target lets sigma permute {0,...,r-1} and quantifies 0<=i<r, with a translator disclosure",
        "target_lines": "269-281",
        "target_path": "source/id-ID/chapter2-unit-024.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.glimpse-of-lattice-theory"
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      "unit_links": [
        {
          "title": "Sekilas tentang Teori Kisi",
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        "source_line": "670-673",
        "source_path": "chapter2.tex",
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        "target_claim": "The target assumes a<=b and discloses the correction so the zero-length case is included",
        "target_lines": "319-330",
        "target_path": "source/id-ID/chapter2-unit-024.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.glimpse-of-lattice-theory"
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      "unit_links": [
        {
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        "source_line": "710",
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        "target_claim": "The target uses [y_{i+1},y_i] and assigns y_{i+1}=a and y_i=b, with a translator disclosure",
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        "target_path": "source/id-ID/chapter2-unit-024.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.glimpse-of-lattice-theory"
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      "unit_links": [
        {
          "title": "Sekilas tentang Teori Kisi",
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      "discovery_scope": "exact_target_file",
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        "source_line": "800",
        "source_path": "chapter2.tex",
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        "target_claim": "The target uses r:X->X' and discloses the corrected direction in a translator note",
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.direct-sum-decomposition"
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      "unit_links": [
        {
          "title": "Dekomposisi Jumlah Langsung",
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      "discovery_scope": "exact_target_file",
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        "source_line": "987",
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        "target_claim": "The target declares (X'_i) and (Y'_i) and discloses the correction in a translator note",
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
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      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
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      "discovery_scope": "exact_target_file",
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        "source_line": "998",
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems"
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      "unit_links": [
        {
          "title": "Subobjek dan Teorema Isomorfisme",
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      "discovery_scope": "exact_target_file",
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        "source_line": "1527",
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        "target_claim": "The target uses H:X\\mapsto[X\\xrightarrow{\\identity_X}X] and discloses the repair in a translator footnote",
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      "related_native": {},
      "unit_ids": [
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      "unit_links": [
        {
          "title": "Funktor Eksak, Objek Injektif, dan Projektif",
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    {
      "discovery_scope": "exact_target_file",
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      "id": "O014-C028",
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        "source_line": "1719",
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        "target_claim": "The target uses \\mathrm{K}_0(F) and discloses the corrected functor name in a translator footnote",
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        "target_path": "source/id-ID/chapter2-unit-029.tex"
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      "unit_ids": [
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        {
          "title": "Subkategori Serre dan Grup K0",
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      "discovery_scope": "exact_target_file",
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      "native": {
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        "evidence": "Pinned chapter2.tex lines 1653-1661; direct verification of the localization universal property and the canonical fiber-product roof",
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        "source_line": "1657-1661",
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        "target_lines": "240-260",
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      "unit_ids": [
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        {
          "title": "Subkategori Serre dan Grup K0",
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    {
      "discovery_scope": "exact_target_file",
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        "source_line": "10",
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        "status": "accepted_disclosed",
        "target_claim": "The target restores the intended transition 'Sebaliknya' and discloses the malformed source fragment",
        "target_lines": "21-27",
        "target_path": "source/id-ID/chapter3-unit-031.tex"
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      "related_native": {},
      "unit_ids": [
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      "unit_links": [
        {
          "title": "Kompleks",
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    {
      "discovery_scope": "exact_target_file",
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      "id": "O014-C031",
      "kind": "corrections",
      "native": {
        "classification": "mathematical_sequence_typo",
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        "evidence": "Pinned chapter3.tex lines 26-33, especially the displayed resolution at line 27 and diagram at lines 29-32",
        "rationale": "A cochain resolution has successive degrees, and the immediately following diagram displays I^0 -> I^1 -> I^2 in that order.",
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        "source_line": "27",
        "source_path": "chapter3.tex",
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        "target_claim": "The target restores I^1 between I^0 and I^2 and discloses the repair",
        "target_lines": "98-109",
        "target_path": "source/id-ID/chapter3-unit-031.tex"
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      "unit_ids": [
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        {
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    {
      "discovery_scope": "exact_target_file",
      "flags": [
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      "id": "O014-C032",
      "kind": "corrections",
      "native": {
        "classification": "mathematical_index_typo",
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        "evidence": "Pinned chapter3.tex line 10; prelude-unit-001.tex lines 60 and 74-78; chapter2-unit-022.tex lines 234-243; chapter2-unit-026.tex lines 53-55",
        "rationale": "Under the source convention d^{n-1}:X^{n-1}->X^n and d^n:X^n->X^{n+1}, Image(d^{n-1}) is the subobject of Ker(d^n); Image(d^{n+1}) lies in X^{n+2} and cannot be its denominator.",
        "source_claim": "The cohomology quotient is printed Ker(d^n)/Image(d^{n+1})",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "10",
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        "o014.aljabr2.chapter3.overview"
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        {
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      "unit_ids": [
        "o014.aljabr2.chapter3.hom-complex-and-homotopy"
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      "unit_links": [
        {
          "title": "Kompleks Hom dan Homotopi",
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        "o014.aljabr2.chapter3.hom-complex-and-homotopy"
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        {
          "title": "Kompleks Hom dan Homotopi",
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        "source_line": "343",
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        "o014.aljabr2.chapter3.hom-complex-and-homotopy"
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        {
          "title": "Kompleks Hom dan Homotopi",
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      "unit_ids": [
        "o014.aljabr2.chapter3.opposite-category-complexes"
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        {
          "title": "Kompleks pada kategori lawan",
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        "source_line": "635",
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        "o014.aljabr2.chapter3.opposite-category-complexes"
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        {
          "title": "Kompleks pada kategori lawan",
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        "o014.aljabr2.chapter3.double-complexes"
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        {
          "title": "Bikompleks",
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        "source_line": "915-941",
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        "source_line": "964",
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        "source_line": "971",
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      "unit_ids": [
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      "discovery_scope": "exact_target_file",
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        "source_line": "1026-1031",
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      "discovery_scope": "exact_target_file",
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        "source_line": "1388",
        "source_path": "chapter3.tex",
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      "unit_ids": [
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      "discovery_scope": "exact_target_file",
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        "source_line": "1397",
        "source_path": "chapter3.tex",
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        "target_claim": "The target writes b_{n+1}^* as the map corresponding to d^n and discloses the corrected index",
        "target_lines": "236-240",
        "target_path": "source/id-ID/chapter3-unit-039.tex"
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        {
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        "classification": "notation_argument_declaration_omission",
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        "rationale": "The algebra R is a genuine parameter of the bar construction and the later cyclic-cohomology correction requires coefficients other than R. Declaring the two-argument notation makes line 1398 and the coefficient-sensitive SBI sequence unambiguous while preserving the source's regular-coefficient abbreviations.",
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        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1398",
        "source_path": "chapter3.tex",
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        "target_claim": "The target explicitly defines HH_n(R,M) and HH^n(R,M), abbreviates the regular-coefficient case as HH_n(R) and HH^n(R), and discloses the omitted notation declaration",
        "target_lines": "241-249",
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      "unit_ids": [
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      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C047",
      "kind": "corrections",
      "native": {
        "classification": "complex_argument_order_typo",
        "correction_id": "O014-C047",
        "evidence": "Pinned chapter3.tex lines 1365-1371 and 1401-1404; direct comparison with the defining argument order",
        "rationale": "The complexes were defined as C_bullet(R,M) and C^bullet(R,M), with the algebra first and coefficient bimodule second. A general R-module M is not an algebra, so the reversed expressions are not defined by the construction.",
        "source_claim": "For a commutative algebra R and an arbitrary R-module M, the source reverses the arguments and writes C_bullet(M,R) and C^bullet(M,R)",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1402",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target writes C_bullet(R,M) and C^bullet(R,M) to match their definitions and discloses the argument-order correction",
        "target_lines": "255-260",
        "target_path": "source/id-ID/chapter3-unit-039.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C048",
      "kind": "corrections",
      "native": {
        "classification": "homology_cohomology_terminology_typo",
        "correction_id": "O014-C048",
        "evidence": "Pinned chapter3.tex lines 1487, 1525-1529, and 1545-1566; direct comparison with the displayed homological degrees",
        "rationale": "The cyclic bicomplexes are explicitly treated as chain double complexes, and the three groups identified in the sentence are HH_n(R), HC_n(R), and HC_{n-2}(R). Thus the relevant functor is H_n, not H^n.",
        "source_claim": "The proof calls the degree-n groups of three total chain complexes their n-th cohomology",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1566",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target calls them n-th homology groups and discloses the homology/cohomology correction",
        "target_lines": "650-656",
        "target_path": "source/id-ID/chapter3-unit-039.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C049",
      "kind": "corrections",
      "native": {
        "classification": "coefficient_bimodule_error",
        "correction_id": "O014-C049",
        "evidence": "Pinned chapter3.tex lines 1353-1362, 1378-1382, and 1574-1580; natural currying F(r_0,...,r_q) <-> [f(r_1,...,r_q)(r_0)] and direct verification of the contragredient bimodule actions",
        "rationale": "The degree-q scalar-dual column is Hom_k(R^{tensor(q+1)},k), naturally isomorphic by tensor-Hom adjunction to Hom_k(R^{tensor q},R^vee)=C^q(R,R^vee). It is not C^q(R,R) without an additional bimodule self-duality R isomorphic to R^vee. No finite-generation or projectivity hypothesis is needed, and the explicit k-linear bar contraction dualizes directly.",
        "source_claim": "After defining CC'(R) componentwise as Hom_k(CC(R),k), the source writes the cohomological SBI middle term as HH^{n+1}(R), which earlier means HH^{n+1}(R,R)",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1574-1580",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target defines R^vee=Hom_k(R,k) with (r phi r')(x)=phi(r'xr), writes the SBI middle term as HH^{n+1}(R,R^vee), and discloses the coefficient correction",
        "target_lines": "684-700",
        "target_path": "source/id-ID/chapter3-unit-039.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology"
      ],
      "unit_links": [
        {
          "title": "Latihan: Homologi dan Kohomologi Hochschild",
          "unit_id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-039"
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    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
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      "id": "O014-C050",
      "kind": "corrections",
      "native": {
        "classification": "missing_hypothesis",
        "correction_id": "O014-C050",
        "evidence": "Pinned chapter3.tex lines 1588 and 1605-1616; direct categorical counterexample and two independent mathematical audits",
        "rationale": "For a non-Abelian additive category the claim fails; for example, in finite free abelian groups multiplication by 2 on Z[0] is monic and epic in the bounded-complex category but is not an isomorphism. The source itself strengthens A to Abelian only at line 1616.",
        "source_claim": "The source says C^+(A), C^-(A), and C^b(A) are Abelian subcategories although A has only been assumed additive",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1605",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target makes the Abelian-subcategory assertion conditional on A being Abelian and discloses the added hypothesis",
        "target_lines": "37-44",
        "target_path": "source/id-ID/chapter3-unit-040.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.truncation-functors"
      ],
      "unit_links": [
        {
          "title": "Funktor pemenggalan",
          "unit_id": "o014.aljabr2.chapter3.truncation-functors",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-040"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C051",
      "kind": "corrections",
      "native": {
        "classification": "ambiguous_antecedent",
        "correction_id": "O014-C051",
        "evidence": "Pinned chapter3.tex lines 1622-1644; direct comparison of the diagram, transition paragraph, and cohomology formulas",
        "rationale": "The displayed cohomology formulas apply to the two vertical comparison maps defined in the truncation diagram; transition maps between different cutoffs can change cohomology in the intervening degrees.",
        "source_claim": "The lemma says the above morphisms induce cohomology isomorphisms immediately after transition maps indexed by m<=n, although those transition maps are not generally quasi-isomorphisms",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1637-1644",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target explicitly identifies the two vertical comparison maps tau^{<=n}X to tilde-tau^{<=n}X and tilde-tau^{>=n}X to tau^{>=n}X",
        "target_lines": "118-125",
        "target_path": "source/id-ID/chapter3-unit-040.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.truncation-functors"
      ],
      "unit_links": [
        {
          "title": "Funktor pemenggalan",
          "unit_id": "o014.aljabr2.chapter3.truncation-functors",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-040"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C052",
      "kind": "corrections",
      "native": {
        "classification": "component_type_imprecision",
        "correction_id": "O014-C052",
        "evidence": "Pinned chapter3.tex lines 1626, 1632, and 1654-1657; direct degree and domain typing",
        "rationale": "By the defining diagram, the degree-n term of tilde-tau^{<=n-1}X is Coim(d^{n-1}), not Image(d^{n-1}); the category is Abelian, so the canonical comparison Coim to Image is an isomorphism and repairs the typed component map.",
        "source_claim": "The proof calls the degree-n component of tilde-tau^{<=n-1}X the map Image(d^{n-1}) to Ker(d^n)",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1656",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target writes Coim(d^{n-1}) isomorphic to Image(d^{n-1}) and then included in Ker(d^n), with the canonical identification disclosed",
        "target_lines": "147-152",
        "target_path": "source/id-ID/chapter3-unit-040.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.truncation-functors"
      ],
      "unit_links": [
        {
          "title": "Funktor pemenggalan",
          "unit_id": "o014.aljabr2.chapter3.truncation-functors",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-040"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C053",
      "kind": "corrections",
      "native": {
        "classification": "object_category_typo",
        "correction_id": "O014-C053",
        "evidence": "Pinned chapter3.tex lines 1616-1632 and 1702-1708; direct typing of both sides and two independent mathematical audits",
        "rationale": "The truncation functors and H^n are defined on complexes. Interpreting an object of A as a degree-zero complex makes the printed statement needlessly restrictive and misses the intended arbitrary-complex identity.",
        "source_claim": "The double-truncation proposition quantifies X in Obj(A)",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1703",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target quantifies X in Obj(C(A)) and discloses the corrected object category",
        "target_lines": "259-262",
        "target_path": "source/id-ID/chapter3-unit-040.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.truncation-functors"
      ],
      "unit_links": [
        {
          "title": "Funktor pemenggalan",
          "unit_id": "o014.aljabr2.chapter3.truncation-functors",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-040"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C054",
      "kind": "corrections",
      "native": {
        "classification": "object_functor_type_error",
        "correction_id": "O014-C054",
        "evidence": "Pinned chapter3.tex lines 1719-1732; direct object/functor typing and two independent mathematical audits",
        "rationale": "Each left-hand side and the following explicit complex are objects depending on X whereas H^p composed with F_I and H^q composed with F_II are functors until evaluated.",
        "source_claim": "The source equates the object H_I^p(X) or H_II^q(X) with the corresponding unapplied composite functor",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1721; 1728",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target evaluates both composite functors at X and discloses the paired correction",
        "target_lines": "34-49",
        "target_path": "source/id-ID/chapter3-unit-041.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complex-cohomology"
      ],
      "unit_links": [
        {
          "title": "Kohomologi bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complex-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-041"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C055",
      "kind": "corrections",
      "native": {
        "classification": "quasi_isomorphism_label_error",
        "correction_id": "O014-C055",
        "evidence": "Pinned chapter3.tex lines 1832-1838 and 1849-1859; direct comparison of the hypothesis diagram and induction argument and an independent mathematical audit",
        "rationale": "The theorem hypothesis and line 1838 imply that H_I^q(f) is a quasi-isomorphism; the subsequent long-exact-sequence and Five-Lemma argument uses only induced cohomology isomorphisms and does not establish a chain-level isomorphism.",
        "source_claim": "The right vertical arrow is labeled with an isomorphism symbol although the hypothesis provides only a quasi-isomorphism of complexes",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1851",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target names the arrow H_I^q(f)[-q] and explicitly labels it a quasi-isomorphism",
        "target_lines": "298-307",
        "target_path": "source/id-ID/chapter3-unit-041.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complex-cohomology"
      ],
      "unit_links": [
        {
          "title": "Kohomologi bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complex-cohomology",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-041"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C056",
      "kind": "corrections",
      "native": {
        "classification": "undefined_boundary_index",
        "correction_id": "O014-C056",
        "evidence": "Pinned chapter3.tex lines 1918-1920; direct degree typing and two independent mathematical audits",
        "rationale": "At the base step the partial resolution is X to I^0, so its cokernel is Coker[X to I^0]; I^{-1} has not been defined.",
        "source_claim": "The recursion includes n=0 but writes Coker[I^{n-1} to I^n], introducing undefined I^{-1}",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "1920",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target uses Coker[X to I^0] at n=0 and the printed formula only for n>=1",
        "target_lines": "61-65",
        "target_path": "source/id-ID/chapter3-unit-042.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.resolutions"
      ],
      "unit_links": [
        {
          "title": "Resolusi",
          "unit_id": "o014.aljabr2.chapter3.resolutions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-042"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C057",
      "kind": "corrections",
      "native": {
        "classification": "diagram_domain_typo",
        "correction_id": "O014-C057",
        "evidence": "Pinned chapter3.tex lines 2035-2038; direct domain typing and two independent mathematical audits",
        "rationale": "The maps d_X^n, alpha^n, and h^n all have domain X^n; the neighboring node is X^{n+1}.",
        "source_claim": "A diagram node is printed as X while its outgoing and incoming maps are indexed in degree n",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "2037",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target labels the node X^n and discloses the repair",
        "target_lines": "217-221",
        "target_path": "source/id-ID/chapter3-unit-042.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.resolutions"
      ],
      "unit_links": [
        {
          "title": "Resolusi",
          "unit_id": "o014.aljabr2.chapter3.resolutions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-042"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C058",
      "kind": "corrections",
      "native": {
        "classification": "matrix_type_error",
        "correction_id": "O014-C058",
        "evidence": "Pinned chapter3.tex lines 2139-2151; direct matrix typing and two independent mathematical audits",
        "rationale": "The matrix acts from I^n direct-sum C^n, so its lower-right differential must be d_C^n; this makes the composition typed and yields delta=theta eta.",
        "source_claim": "The lower-right entry of the left matrix is printed d_K^n",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "2144",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target restores d_C^n and discloses the repair",
        "target_lines": "353-369",
        "target_path": "source/id-ID/chapter3-unit-042.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.resolutions"
      ],
      "unit_links": [
        {
          "title": "Resolusi",
          "unit_id": "o014.aljabr2.chapter3.resolutions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-042"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C059",
      "kind": "corrections",
      "native": {
        "classification": "bicomplex_direction_error",
        "correction_id": "O014-C059",
        "evidence": "Pinned chapter3.tex lines 2178-2193; direct bidegree typing and two independent mathematical audits",
        "rationale": "The vertical resolution maps already have bidegree (0,1); the following requirement d_h^2=0 identifies the intended new maps as horizontal of bidegree (1,0).",
        "source_claim": "The construction of the horizontal differential repeats the vertical map I^{n,m} to I^{n,m+1}",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "2192",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target restores the horizontal map I^{n,m} to I^{n+1,m} and discloses the repair",
        "target_lines": "431-435",
        "target_path": "source/id-ID/chapter3-unit-042.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.resolutions"
      ],
      "unit_links": [
        {
          "title": "Resolusi",
          "unit_id": "o014.aljabr2.chapter3.resolutions",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-042"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C060",
      "kind": "corrections",
      "native": {
        "classification": "diagram_domain_typo",
        "correction_id": "O014-C060",
        "evidence": "Pinned chapter3.tex lines 2328 and 2343-2348; direct source-definition comparison and independent mathematical review",
        "rationale": "For a short exact sequence 0 to X to Y to Z to 0, the connecting morphisms eta^{n-1} and delta^{n-1} have domains G^{n-1}(Z) and F^{n-1}(Z) and codomains G^n(X) and F^n(X).",
        "source_claim": "The morphism-of-delta-functors square prints G^{n-1}(X) and F^{n-1}(X) in its left column",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "2345-2346",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target restores G^{n-1}(Z) and F^{n-1}(Z) and discloses the repair",
        "target_lines": "181-184",
        "target_path": "source/id-ID/chapter3-unit-043.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.classical-derived-functors"
      ],
      "unit_links": [
        {
          "title": "Funktor turunan klasik",
          "unit_id": "o014.aljabr2.chapter3.classical-derived-functors",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-043"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [
        "accepted_disclosed"
      ],
      "id": "O014-C061",
      "kind": "corrections",
      "native": {
        "classification": "connecting_morphism_degree_typo",
        "correction_id": "O014-C061",
        "evidence": "Pinned chapter3.tex lines 2510-2511 and 2537-2541; direct degree typing and independent mathematical review",
        "rationale": "The displayed arrows have degree-(n-1) domains and degree-n codomains, so the defining connecting morphisms carry superscript n-1; the following prose confirms the composites are F^{n-1}(Z) to F^n(X) and R^{n-1}(Z) to R^n(X).",
        "source_claim": "The terminal comparison square labels maps from F^{n-1}(B) and R^{n-1}(B) with delta_F^n and delta^n",
        "source_commit": "9a5803ff77dd3257484cb177f851a73770a59dd3",
        "source_line": "2538-2539",
        "source_path": "chapter3.tex",
        "status": "accepted_disclosed",
        "target_claim": "The target restores delta_F^{n-1} and delta^{n-1} and discloses the repair",
        "target_lines": "436-443",
        "target_path": "source/id-ID/chapter3-unit-043.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.classical-derived-functors"
      ],
      "unit_links": [
        {
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        "local_order": "9",
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        "alt_text_id": "Diagram kategori: \\Hm{\\left[ X \\to Y \\to Z \\right]} → \\Hm{\\left[ X \\oplus X' \\to Y \\oplus Y' \\to Z \\oplus Z' \\right]} (\\iota); \\Hm{\\left[ X \\oplus X' \\to Y \\oplus Y' \\to Z \\oplus Z' \\right]} → \\Hm{\\left[ X \\to Y \\to Z \\right]} (p); \\Hm{\\left[ X \\oplus X' \\to Y \\oplus Y' \\to Z \\oplus Z' \\right]} → \\…",
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        "local_order": "10",
        "provenance": "id-ID/chapter2-unit-022.tex:189; tikzcd mandiri",
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      "related_native": {},
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        "o014.aljabr2.chapter2.first-look-at-complexes"
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        "alt_text_id": "Diagram komutatif: S' ↠ S; S' → X'; S → X . (h); X' → X . (f).",
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        "local_order": "1",
        "provenance": "id-ID/chapter2-unit-023.tex:24; tikzcd mandiri",
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        {
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        "alt_text_id": "Diagram kategori: S' → X'; S' ↠ S; S → X (h); X' → S (\\alpha); X' → X (f).",
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        "local_order": "2",
        "provenance": "id-ID/chapter2-unit-023.tex:44; tikzcd mandiri",
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      "related_native": {},
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        {
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        "alt_text_id": "Diagram kategori: \\Ker' → \\Ker; \\Ker' → X'; \\Ker → \\Ker''; \\Ker → X; \\Ker'' → X''; X' → Y'; X' → X (f); X → Y; serta 12 panah lain.",
        "diagram_id": "chapter2-unit-023-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter2-unit-023.tex:71; tikzcd mandiri",
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      "related_native": {},
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    },
    {
      "discovery_scope": "exact_target_file",
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      "native": {
        "alt_text_id": "Diagram eksak: 0 → \\Ker(g); \\Ker(g) ↪ X \\dtimes{X''} \\Ker'' (s); \\Ker(g) → \\Ker(g); X \\dtimes{X''} \\Ker'' ↠ \\Ker''; X \\dtimes{X''} \\Ker'' → X; \\Ker'' → X''; \\Ker(g) ↪ X; \\Ker(g) ⇒ Y'; serta 14 panah lain; satu persegi diberi tanda \\Box.",
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        "local_order": "4",
        "provenance": "id-ID/chapter2-unit-023.tex:113; tikzcd mandiri",
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    {
      "discovery_scope": "exact_target_file",
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        "alt_text_id": "Diagram komutatif: X' → X; X' → Y'; X' → \\underline{X'}; X → X''; X → Y; X → \\underline{X}; X'' → 0; X'' → Y''; serta 16 panah lain.",
        "diagram_id": "chapter2-unit-023-d005",
        "local_order": "5",
        "provenance": "id-ID/chapter2-unit-023.tex:176; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
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        {
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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    },
    {
      "discovery_scope": "exact_target_file",
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      "native": {
        "alt_text_id": "Diagram komutatif: \\Ker'' → \\Coker' (\\delta); \\Ker'' → \\underline{\\Ker''} (\\text{morfisme alami); \\Coker' → \\underline{\\Coker'} . (\\text{morfisme alami); \\underline{\\Ker''} → \\underline{\\Coker'} . (\\underline{\\delta).",
        "diagram_id": "chapter2-unit-023-d006",
        "local_order": "6",
        "provenance": "id-ID/chapter2-unit-023.tex:187; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.diagram-lemmas"
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      "unit_links": [
        {
          "title": "Beberapa Lema Diagram",
          "unit_id": "o014.aljabr2.chapter2.diagram-lemmas",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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      ]
    },
    {
      "discovery_scope": "exact_target_file",
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      "native": {
        "alt_text_id": "Diagram komutatif: S' ↠ S (h); S' → \\Ker'; S → \\Ker (\\psi); S → \\Ker'' (0); \\Ker' → \\Ker; \\Ker' ↪ X'; \\Ker ↪ X; \\Ker → \\Ker''; serta 3 panah lain.",
        "diagram_id": "chapter2-unit-023-d007",
        "local_order": "7",
        "provenance": "id-ID/chapter2-unit-023.tex:258; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
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        "o014.aljabr2.chapter2.diagram-lemmas"
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    {
      "discovery_scope": "exact_target_file",
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: S' ↠ S (h); S' → X'; S → X; S → X'' . (0); X' → X (f); X → X'' . (g).",
        "diagram_id": "chapter2-unit-023-d008",
        "local_order": "8",
        "provenance": "id-ID/chapter2-unit-023.tex:268; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
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        {
          "title": "Beberapa Lema Diagram",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter2-unit-023-d009",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: S_0 → \\Ker; S_0 ↠ S; S → \\Ker'' (\\psi); \\Ker → \\Ker''.",
        "diagram_id": "chapter2-unit-023-d009",
        "local_order": "9",
        "provenance": "id-ID/chapter2-unit-023.tex:293; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.diagram-lemmas"
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        {
          "title": "Beberapa Lema Diagram",
          "unit_id": "o014.aljabr2.chapter2.diagram-lemmas",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: S_1 ↠ S; S_1 → X \\dtimes{X''} \\Ker''; S → \\Ker'' (\\psi); S → 0 . (0); X \\dtimes{X''} \\Ker'' → \\Ker''; \\Ker'' → 0 ..",
        "diagram_id": "chapter2-unit-023-d010",
        "local_order": "10",
        "provenance": "id-ID/chapter2-unit-023.tex:303; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.diagram-lemmas"
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter2-unit-023-d011",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: S → \\Ker'' (\\psi); \\Ker'' → \\Coker' (\\delta); \\Coker' ↪ \\Coker' \\dsqcup{Y'} Y; S_1 ↠ S; S_1 → X \\dtimes{X''} \\Ker''; X \\dtimes{X''} \\Ker'' → \\Coker' \\dsqcup{Y'} Y (\\delta_0); X \\dtimes{X''} \\Ker'' → \\Ker''; X \\dtimes{X''} \\Ker'' → X; serta 2 panah lain.",
        "diagram_id": "chapter2-unit-023-d011",
        "local_order": "11",
        "provenance": "id-ID/chapter2-unit-023.tex:317; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter2.diagram-lemmas"
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        {
          "title": "Beberapa Lema Diagram",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: S_0 ↠ S_1; S_0 → X' (k); S_1 → Y' (\\xi); S_1 → \\Coker' . (0); X' → Y'; Y' → \\Coker' ..",
        "diagram_id": "chapter2-unit-023-d012",
        "local_order": "12",
        "provenance": "id-ID/chapter2-unit-023.tex:336; tikzcd mandiri",
        "unit_filename": "chapter2-unit-023.tex"
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      "related_native": {},
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        "o014.aljabr2.chapter2.diagram-lemmas"
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        {
          "title": "Beberapa Lema Diagram",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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    {
      "discovery_scope": "exact_target_file",
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      "native": {
        "alt_text_id": "Diagram komutatif: S_0 ↠ S_1; S_0 → X' (k); S_0 → X (\\lambda); S_1 → Y' (\\xi); S_1 → X \\dtimes{X''} \\Ker''; X \\dtimes{X''} \\Ker'' → X; X' → Y' (a); X' → X (f); serta 2 panah lain.",
        "diagram_id": "chapter2-unit-023-d013",
        "local_order": "13",
        "provenance": "id-ID/chapter2-unit-023.tex:346; tikzcd mandiri",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter2-unit-023"
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    {
      "discovery_scope": "exact_target_file",
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        "alt_text_id": "Diagram kategori: S_0 ↠ S_1; S_0 → \\Ker; S_0 → X (\\lambda -fk); S_1 ↠ S; S → \\Ker'' (\\psi); \\Ker ↪ X; \\Ker → \\Ker''; \\Ker'' ↪ X'' .; serta 1 panah lain.",
        "diagram_id": "chapter2-unit-023-d014",
        "local_order": "14",
        "provenance": "id-ID/chapter2-unit-023.tex:360; tikzcd mandiri",
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    {
      "discovery_scope": "exact_target_file",
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        "alt_text_id": "Diagram kategori: S_0 ↠ S_1; S_0 → X (\\lambda); S_1 ↠ S; S_1 → X \\dtimes{X''} \\Ker''; S → \\Ker'' (\\psi); X \\dtimes{X''} \\Ker'' → \\Ker''; X \\dtimes{X''} \\Ker'' → X; \\Ker'' → X'' .; serta 1 panah lain.",
        "diagram_id": "chapter2-unit-023-d015",
        "local_order": "15",
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        "local_order": "16",
        "provenance": "id-ID/chapter2-unit-023.tex:393; tikzcd mandiri",
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        "alt_text_id": "Diagram komutatif: S' ↠ S; S' → X_2; S → X_3 . (h); X_2 → X_3 ..",
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    {
      "discovery_scope": "exact_target_file",
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        "alt_text_id": "Diagram komutatif: S''' ↠ S''; S''' → X_1; S'' ↠ S'; S'' → Y_1; S' → X_2; X_2 → Y_2 . (f_2); X_1 → Y_1 (f_1); Y_1 → Y_2 ..",
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        "alt_text_id": "Diagram kategori: S''' ↠ S'; S''' → X_1; S' ↠ S; S' → X_2; S → X_3 (h); X_1 → X_2; X_1 → Y_1 (f_1); X_2 → X_3; serta 3 panah lain.",
        "diagram_id": "chapter2-unit-023-d019",
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      "discovery_scope": "exact_target_file",
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        "alt_text_id": "Diagram TikZ; 1 untai, sisi, atau panah digambar menurut komposisi. Konteks: persegi kiri atas. Komposisikan kedua lintasan",
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        "local_order": "6",
        "provenance": "id-ID/chapter3-unit-034.tex:372; tikzcd mandiri",
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      "native": {
        "alt_text_id": "Diagram komutatif: X → X (\\identity_X); X → Y (f); Y → \\Cyl(f) (\\phi); Y → \\Cone(f) (\\alpha(f)); \\Cone(f) → \\Cone(f) (\\identity_{\\Cone(f)}); X → \\Cyl(f); \\Cyl(f) → \\Cone(f).",
        "diagram_id": "chapter3-unit-034-d007",
        "local_order": "7",
        "provenance": "id-ID/chapter3-unit-034.tex:376; tikzcd mandiri",
        "unit_filename": "chapter3-unit-034.tex"
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      "related_native": {},
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-034"
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: s_{1,X}^n : \\sigma(X{[1]})^n = X^{1-n} → X^{1-n} = (\\sigma X){[-1]}^n . (\\sim).",
        "diagram_id": "chapter3-unit-035-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter3-unit-035.tex:58; tikzcd mandiri; label=eqn:sigma-s",
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      "native": {
        "alt_text_id": "Diagram kategori: \\sigma\\left( X{[1]} \\right) → \\sigma\\left(\\Cone(f)\\right) (\\sigma(\\beta(f))); \\sigma\\left( X{[1]} \\right) → (\\sigma X){[-1]} }\"' inner sep=0.6em] (s_{1,X}); \\sigma\\left(\\Cone(f)\\right) → \\sigma Y (\\sigma(\\alpha(f))); \\sigma\\left(\\Cone(f)\\right) → \\Cone(\\sigma(f)){[-1]} }\"' inner s…",
        "diagram_id": "chapter3-unit-035-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter3-unit-035.tex:137; tikzcd mandiri",
        "unit_filename": "chapter3-unit-035.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.opposite-category-complexes"
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      "unit_links": [
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          "title": "Kompleks pada kategori lawan",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-035"
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      "native": {
        "alt_text_id": "Diagram kategori: (\\sigma Y)^n → (\\sigma(X[1]))^{n+1}; (\\sigma(X[1]))^{n+1} → (\\sigma X)[-1]^{n+1} (\\sim); Y^{-n} → (\\sigma Y)^n; Y^{-n} → X^{-n} ((f^{-n})^{\\opp}); X^{-n} → (\\sigma(X[1]))^{n+1}; X^{-n} → X^{-n} (s_{1, X}^{n+1} = (-1)^n); X^{-n} → (\\sigma X)[-1]^{n+1}.",
        "diagram_id": "chapter3-unit-035-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter3-unit-035.tex:169; tikzcd mandiri",
        "unit_filename": "chapter3-unit-035.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.opposite-category-complexes"
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        "alt_text_id": "Diagram kategori: \\cdots → X^{p, q+1}; X^{p, q+1} → X^{p+1, q+1}; X^{p, q+1} → \\vdots; X^{p+1, q+1} → \\cdots; X^{p+1, q+1} → \\vdots; \\cdots → X^{p, q}; X^{p, q} → X^{p+1, q} (\\dhori^{p,q}); X^{p, q} → X^{p, q+1} (\\dvert^{p,q}); serta 4 panah lain.",
        "diagram_id": "chapter3-unit-036-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter3-unit-036.tex:57; tikzcd mandiri",
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        "alt_text_id": "Diagram kategori: (F_{\\mathrm{II}} X)^q → simpul di atas (d^q_{F_{\\mathrm{II}} X}); \\cdots → X^{p,q}; X^{p,q} → \\cdots (\\dhori^{p,q}); X^{p,q} → {} (\\dvert^{p,q}); \\vdots → (F_{\\mathrm{II}} X)^q; {} → X^{p,q}; \\cdots → (F_{\\mathrm{I}} X)^p; (F_{\\mathrm{I}} X)^p → \\cdots (d^p_{F_{\\mathrm{I}} X}).",
        "diagram_id": "chapter3-unit-036-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter3-unit-036.tex:87; tikzcd mandiri; label=eqn:bicplx-diagram",
        "unit_filename": "chapter3-unit-036.tex"
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      "id": "chapter3-unit-036-d003",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: X^{p,q} → X^{p,q} ((-1)^{pq} \\identity); X^{p,q} → X^{p+1, q} \\oplus X^{p, q+1} ( (\\dhori, (-1)^p \\dvert) ); X^{p+1, q} \\oplus X^{p, q+1} → X^{p+1, q} \\oplus X^{p, q+1} (((-1)^{(p+1)q} \\identity, (-1)^{p(q+1)} \\i…); X^{p,q} → X^{p+1, q} \\oplus X^{p, q+1} (((-1)^q \\dhori, \\dvert)).",
        "diagram_id": "chapter3-unit-036-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter3-unit-036.tex:178; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
      "unit_ids": [
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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      "native": {
        "alt_text_id": "Diagram kategori: \\tot_{\\oplus} \\left( X[1]_{\\mathrm{I}}[1]_{\\mathrm{II}}\\right) _{\\mathr… → \\tot_{\\oplus}\\left(X[1]_{\\mathrm{II}}\\right)[1] }\"]; \\tot_{\\oplus} \\left( X[1]_{\\mathrm{I}}[1]_{\\mathrm{II}}\\right) _{\\mathr… → \\tot_{\\oplus} \\left( X[1]_{\\mathrm{I}}\\right)[1] }\"' inner sep=0.6em]; \\tot_{\\…",
        "diagram_id": "chapter3-unit-036-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter3-unit-036.tex:257; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
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          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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      "discovery_scope": "exact_target_file",
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      "id": "chapter3-unit-036-d005",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: \\tot_{\\oplus} \\left( X[1]_{\\mathrm{I}}[1]_{\\mathrm{II}} \\right) _{\\math… → \\tot_{\\oplus}(X)[2] }\"] (\\text{$\\theta$ lalu $\\theta'$); \\tot_{\\oplus} \\left( X[1]_{\\mathrm{I}}[1]_{\\mathrm{II}} \\right) _{\\math… → \\tot_{\\oplus}\\left( \\mathrm{swap}(X)[1]_{\\mathrm{I}}[1]_{\\mathrm{II}} \\…;…",
        "diagram_id": "chapter3-unit-036-d005",
        "local_order": "5",
        "provenance": "id-ID/chapter3-unit-036.tex:263; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: X^{p+1, q+1} → X^{p+1, q+1} ((-1)^p \\identity); X^{p+1, q+1} → X^{p+1, q+1} (\\identity); X^{p+1, q+1} → X^{p+1, q+1} ((-1)^{p+1} \\identity).",
        "diagram_id": "chapter3-unit-036-d006",
        "local_order": "6",
        "provenance": "id-ID/chapter3-unit-036.tex:280; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
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        {
          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\cate{C}^2 F: \\cate{C}(\\mathcal{A}_1) \\times \\cate{C}(\\mathcal{A}_2) → \\cate{C}^2(\\mathcal{B}); (X, Y) → (F(X, Y))^{p, q} := F(X^p, Y^q).",
        "diagram_id": "chapter3-unit-036-d007",
        "local_order": "7",
        "provenance": "id-ID/chapter3-unit-036.tex:332; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
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          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-036-d008",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: X^{p,q} → Y^{p-1, q} (h^{p,q}); X^{p,q} → Y^{p, q-1} (k^{p, q}).",
        "diagram_id": "chapter3-unit-036-d008",
        "local_order": "8",
        "provenance": "id-ID/chapter3-unit-036.tex:366; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
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        {
          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\cate{C}(\\mathcal{A})^{\\opp} \\times \\cate{C}(\\mathcal{A}) → \\cate{C}(\\mathcal{A}) \\times \\cate{C}(\\mathcal{A})^{\\opp} (\\simeq); \\cate{C}(\\mathcal{A})^{\\opp} \\times \\cate{C}(\\mathcal{A}) → \\cate{C}(\\mathcal{A}^{\\opp}) \\times \\cate{C}(\\mathcal{A}) ((\\sigma^{-1}, \\identity)); \\cate{C…",
        "diagram_id": "chapter3-unit-036-d009",
        "local_order": "9",
        "provenance": "id-ID/chapter3-unit-036.tex:464; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
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          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-036-d010",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\Hom^{p-1, q}(X, Y) → \\Hom^{p, q}(X, Y) (\\dhori^{p-1, q}); \\Hom^{p, q-1}(X, Y) . → \\Hom^{p, q}(X, Y) ((-1)^p \\dvert^{p, q-1}).",
        "diagram_id": "chapter3-unit-036-d010",
        "local_order": "10",
        "provenance": "id-ID/chapter3-unit-036.tex:496; tikzcd mandiri",
        "unit_filename": "chapter3-unit-036.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.double-complexes"
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          "title": "Bikompleks",
          "unit_id": "o014.aljabr2.chapter3.double-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-036"
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: \\Ker(d_X^n) ↠ \\Hm^n(X); \\Ker(d_X^n) → \\Ker(d_Y^n) (\\text{diinduksi oleh $f$); \\Hm^n(X) ↪ \\Coker(d_X^{n-1}); \\Hm^n(X) → \\Hm^n(Y) (\\Hm^n(f)); \\Coker(d_X^{n-1}) → \\Coker(d_Y^{n-1}) . (\\text{diinduksi oleh $f$); \\Ker(d_Y^n) ↠ \\Hm^n(Y); \\Hm^n(Y) ↪ \\Coker(d_Y^{n-1}) ..",
        "diagram_id": "chapter3-unit-037-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter3-unit-037.tex:109; tikzcd mandiri; label=eqn:induced-morphism-cohomology",
        "unit_filename": "chapter3-unit-037.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.abelian-category-complexes"
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          "title": "Kompleks pada kategori abelian",
          "unit_id": "o014.aljabr2.chapter3.abelian-category-complexes",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-037"
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram eksak: \\cdots → \\Hm^{n-1}(Y); \\Hm^{n-1}(Y) → \\Hm^{n-1}(Z) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshi… (\\Hm^{n-1}(g)); \\Hm^{n-1}(Z) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshi… → \\Hm^n(X) (\\delta^{n-1}); \\Hm^n(X) → \\Hm^n(Y) (\\Hm^n(f)); \\Hm^n(Y) → \\Hm^n(Z) \\tikz…",
        "diagram_id": "chapter3-unit-037-d002",
        "local_order": "2",
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      "related_native": {
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          "description_id": "Barisan eksak panjang: … → H^(n−1)(Y) → H^(n−1)(Z) → H^n(X) → H^n(Y) → H^n(Z) → H^(n+1)(X) → …. Panah berturut-turut berlabel H^(n−1)(g), δ^(n−1), H^n(f), H^n(g), dan δ^n.",
          "diagram_id": "chapter3-unit-037-d002",
          "source_ref": "source/id-ID/chapter3-unit-037.tex:143-162"
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      "unit_links": [
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-037"
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        "alt_text_id": "Diagram komutatif: 0 → X; X → Y; X → \\underline{X}; Y → Z; Y → \\underline{Y}; Z → \\underline{Z}; Z → 0; 0 → \\underline{X}; serta 3 panah lain.",
        "diagram_id": "chapter3-unit-037-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter3-unit-037.tex:167; tikzcd mandiri",
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          "unit_id": "o014.aljabr2.chapter3.abelian-category-complexes",
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: \\cdots → \\Hm^n(X); \\Hm^n(X) → \\Hm^n(\\underline{X}); \\Hm^n(X) → \\Hm^n(Y); \\Hm^n(Y) → \\Hm^n(Z); \\Hm^n(Y) → \\Hm^n(\\underline{Y}); \\Hm^n(Z) → \\Hm^{n+1}(X); \\Hm^n(Z) → \\Hm^n(\\underline{Z}); \\Hm^{n+1}(X) → \\cdots; serta 6 panah lain.",
        "diagram_id": "chapter3-unit-037-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter3-unit-037.tex:173; tikzcd mandiri",
        "unit_filename": "chapter3-unit-037.tex"
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      "related_native": {},
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      "unit_links": [
        {
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        "diagram_id": "chapter3-unit-039-d008",
        "local_order": "8",
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        "alt_text_id": "Diagram eksak: 0 → \\text{kolom ke-$0$}; \\text{kolom ke-$0$} → \\tot\\left(\\sigma_{\\mathrm{I},[0,1]}\\mathrm{CC}(R)\\right); \\tot\\left(\\sigma_{\\mathrm{I},[0,1]}\\mathrm{CC}(R)\\right) → \\text{kolom ke-$1$}; \\text{kolom ke-$1$} → 0.; C_\\bullet(R,R) → \\text{kolom ke-$0$} (\\sim); \\mathsf{B}'R → \\text{kolom k…",
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        "local_order": "1",
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        "local_order": "2",
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        "local_order": "1",
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        "local_order": "2",
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        "local_order": "3",
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        "diagram_id": "chapter3-unit-046-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter3-unit-046.tex:261; tikzcd mandiri; label=eqn:K-injective-projlimit-aux",
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        "alt_text_id": "Diagram eksak: \\displaystyle\\varprojlim_k \\displaystyle\\prod_n \\Hom\\left( X^n, I_k^{n-… → \\displaystyle\\varprojlim_k \\displaystyle\\prod_n \\Hom\\left( X^n, I_k^n \\…; \\displaystyle\\varprojlim_k \\displaystyle\\prod_n \\Hom\\left( X^n, I_k^n \\… → \\displaystyle\\varprojlim_k \\displaystyle\\prod_n \\Hom\\left( X…",
        "diagram_id": "chapter3-unit-046-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter3-unit-046.tex:290; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
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      "unit_links": [
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      "native": {
        "alt_text_id": "Diagram kategori: \\displaystyle\\prod_n \\varprojlim_k \\Hom\\left( X^n, I_k^{n-1} \\right) → \\displaystyle\\prod_n \\varprojlim_k \\Hom\\left( X^n, I_k^n \\right); \\displaystyle\\prod_n \\varprojlim_k \\Hom\\left( X^n, I_k^n \\right) → \\displaystyle\\prod_n \\varprojlim_k \\Hom\\left( X^n, I_k^{n+1} \\right); \\displa…",
        "diagram_id": "chapter3-unit-046-d005",
        "local_order": "5",
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        "unit_filename": "chapter3-unit-046.tex"
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      "related_native": {},
      "unit_ids": [
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          "title": "Kompleks K-injektif dan K-projektif",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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      "native": {
        "alt_text_id": "Diagram kategori: \\cdots → I_2; I_2 → I_1; I_1 → I_0; \\cdots → \\tau^{\\geq -2} A; \\tau^{\\geq -2} A → I_2 (f_2); \\tau^{\\geq -2} A → \\tau^{\\geq -1} A; \\tau^{\\geq -1} A → \\tau^{\\geq 0} A; \\tau^{\\geq -1} A → I_1 (f_1); serta 1 panah lain.",
        "diagram_id": "chapter3-unit-046-d006",
        "local_order": "6",
        "provenance": "id-ID/chapter3-unit-046.tex:333; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
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      "related_native": {},
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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        "alt_text_id": "Diagram kategori: 0 → J; J → I_{k+1}; I_{k+1} → I_k; I_k → 0; 0 → H; H → \\tau^{\\geq-k-1}A; H → J (g); \\tau^{\\geq-k-1}A → I_{k+1} (f_{k+1}); serta 3 panah lain.",
        "diagram_id": "chapter3-unit-046-d007",
        "local_order": "7",
        "provenance": "id-ID/chapter3-unit-046.tex:380; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: I ↪ \\displaystyle\\prod_k I_k; I → \\Cone(\\Delta_I)[-1] }\"']; \\Cone(\\Delta_I)[-1] }\"'] → \\displaystyle\\prod_k I_k.",
        "diagram_id": "chapter3-unit-046-d008",
        "local_order": "8",
        "provenance": "id-ID/chapter3-unit-046.tex:432; tikzcd mandiri; label=eqn:K-injective-diagonal",
        "unit_filename": "chapter3-unit-046.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
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      "unit_links": [
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          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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      "discovery_scope": "exact_target_file",
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      "id": "chapter3-unit-046-d009",
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      "native": {
        "alt_text_id": "Diagram komutatif: A ↪ \\displaystyle\\prod_k \\tau^{\\geq -k} A; A → \\Cone(\\Delta_{\\tau A})[-1] }\"']; \\Cone(\\Delta_{\\tau A})[-1] }\"'] → \\displaystyle\\prod_k \\tau^{\\geq -k} A.",
        "diagram_id": "chapter3-unit-046-d009",
        "local_order": "9",
        "provenance": "id-ID/chapter3-unit-046.tex:435; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
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        {
          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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      "discovery_scope": "exact_target_file",
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: I → \\Cone\\left(\\Delta_I\\right)[-1] (\\text{seperti pada \\eqref{eqn:K-injective-d…); A → \\Cone\\left( \\Delta_{\\tau A} \\right)[-1] .; A → I (f); \\Cone\\left( \\Delta_{\\tau A} \\right)[-1] . → \\Cone\\left(\\Delta_I\\right)[-1] (\\text{diinduksi oleh semua $f_k$).",
        "diagram_id": "chapter3-unit-046-d010",
        "local_order": "10",
        "provenance": "id-ID/chapter3-unit-046.tex:455; tikzcd mandiri; label=eqn:K-injective-A-I",
        "unit_filename": "chapter3-unit-046.tex"
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      "related_native": {
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          "description_id": "Diagram komutatif berbentuk persegi. Baris atas adalah I → Cone(Δ_I)[−1], seperti pada persamaan K-injective-diagonal. Baris bawah adalah A → Cone(Δ_(τA))[−1]. Panah vertikal kiri ialah f: A → I; panah vertikal kanan diinduksi oleh semua f_k.",
          "diagram_id": "chapter3-unit-046-d010",
          "source_ref": "source/id-ID/chapter3-unit-046.tex:453-461"
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      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
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      "unit_links": [
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      "native": {
        "alt_text_id": "Diagram kategori: \\prod_k I_k → \\prod_k I_k (\\Delta_I); \\prod_k I_k → \\Cone\\left(\\Delta_I\\right) (\\alpha(\\Delta_I)); \\prod_k \\tau^{\\geq-k}A → \\prod_k \\tau^{\\geq-k}A (\\Delta_{\\tau A); \\prod_k \\tau^{\\geq-k}A → \\prod_k I_k (\\prod_k f_k); \\prod_k \\tau^{\\geq-k}A → \\Cone\\left(\\Delta_{\\tau A}\\right) (\\alp…",
        "diagram_id": "chapter3-unit-046-d011",
        "local_order": "11",
        "provenance": "id-ID/chapter3-unit-046.tex:483; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
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      "unit_links": [
        {
          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-046-d012",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram eksak: \\cdots \\Hm^n\\left( \\displaystyle\\prod_k I_k \\right) → \\Hm^n\\left( \\Cone(\\Delta_I) \\right); \\Hm^n\\left( \\Cone(\\Delta_I) \\right) → \\Hm^{n+1}\\left( \\displaystyle\\prod_k I_k \\right); \\Hm^{n+1}\\left( \\displaystyle\\prod_k I_k \\right) → \\Hm^{n+1}\\left( \\displaystyle\\prod_k I_k \\right) (\\Hm^…",
        "diagram_id": "chapter3-unit-046-d012",
        "local_order": "12",
        "provenance": "id-ID/chapter3-unit-046.tex:497; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
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      "unit_links": [
        {
          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
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      "id": "chapter3-unit-046-d013",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\prod_{k \\geq -n} \\Hm^n(A) → \\prod_{k \\geq -n} \\Hm^n(A) (\\nabla^n); (a_k)_{k \\geq -n} → (a_{k+1} - a_k)_{k \\geq -n}..",
        "diagram_id": "chapter3-unit-046-d013",
        "local_order": "13",
        "provenance": "id-ID/chapter3-unit-046.tex:569; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
      ],
      "unit_links": [
        {
          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-046-d014",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: \\Hm^n(A) → \\Hm^n {\\Cone(\\Delta_{\\tau A})[-1]}; \\Hm^n(A) ↪ \\prod_{k \\geq -n} \\Hm^n(A) (\\text{morfisme diagonal); \\Hm^n {\\Cone(\\Delta_{\\tau A})[-1]} ↪ \\prod_{k \\geq -n} \\Hm^n(A).",
        "diagram_id": "chapter3-unit-046-d014",
        "local_order": "14",
        "provenance": "id-ID/chapter3-unit-046.tex:593; tikzcd mandiri",
        "unit_filename": "chapter3-unit-046.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.k-injectives"
      ],
      "unit_links": [
        {
          "title": "Kompleks K-injektif dan K-projektif",
          "unit_id": "o014.aljabr2.chapter3.k-injectives",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-046"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-047-d001",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\Cone(f) → X[1] (\\beta(f)); \\Cone(f) → \\Cone(g) (h); Y → \\Cone(f) (\\alpha(f)); Y → \\Cone(g) (\\alpha(g)); \\Cone(g) → X[1] (\\beta(g)).",
        "diagram_id": "chapter3-unit-047-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter3-unit-047.tex:51; tikzcd mandiri",
        "unit_filename": "chapter3-unit-047.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises"
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          "title": "Latihan",
          "unit_id": "o014.aljabr2.chapter3.exercises",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-047"
        }
      ]
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-047-d002",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram eksak: 0 → {A[-n]} }\"]; {A[-n]} }\"] → {B[-n]}; {A[-n]} }\"] → X (\\Psi); {B[-n]} → X (\\exists).",
        "diagram_id": "chapter3-unit-047-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter3-unit-047.tex:150; tikzcd mandiri",
        "unit_filename": "chapter3-unit-047.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises"
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        {
          "title": "Latihan",
          "unit_id": "o014.aljabr2.chapter3.exercises",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-047"
        }
      ]
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-047-d003",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: 0 → M; M → \\widetilde R; \\widetilde R → R (p); R → 0; R → \\widetilde R (s).",
        "diagram_id": "chapter3-unit-047-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter3-unit-047.tex:232; tikzcd mandiri",
        "unit_filename": "chapter3-unit-047.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises"
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        {
          "title": "Latihan",
          "unit_id": "o014.aljabr2.chapter3.exercises",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-047"
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter3-unit-047-d004",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: 0 → D(Z_{n-1}); D(Z_{n-1}) → D(Z_{n-1}) (\\identity); D(Z_{n-1}) → D(B_{n-1}); D(Z_{n-1}) → 0; D(Z_{n-1}) → D(C_n/B_n) (D(d^C_n)); 0 → 0; 0 → D(H_n); 0 → D(B_{n-1}); serta 3 panah lain.",
        "diagram_id": "chapter3-unit-047-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter3-unit-047.tex:534; tikzcd mandiri",
        "unit_filename": "chapter3-unit-047.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter3.exercises"
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      "unit_links": [
        {
          "title": "Latihan",
          "unit_id": "o014.aljabr2.chapter3.exercises",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter3-unit-047"
        }
      ]
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      "discovery_scope": "exact_target_file",
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      "id": "chapter4-unit-048-d001",
      "kind": "diagrams",
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        "alt_text_id": "Diagram kategori: \\cate{K}^+(\\mathcal{A}) → \\cate{K}^+(\\mathcal{A}') (\\cate{K}F); \\cate{K}^+(\\mathcal{A}) → \\cate{D}^+(\\mathcal{A}) (Q); \\cate{K}^+(\\mathcal{A}') → \\cate{D}^+(\\mathcal{A}') (Q'); \\cate{K}^+(\\mathcal{A}') ⇒ \\cate{D}^+(\\mathcal{A}); \\cate{D}^+(\\mathcal{A}) → \\cate{D}^+(\\mathcal{A}') (…",
        "diagram_id": "chapter4-unit-048-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter4-unit-048.tex:115; tikzcd mandiri",
        "unit_filename": "chapter4-unit-048.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter4-unit-048-d002",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\cate{K}^-(\\mathcal{A}) → \\cate{K}^-(\\mathcal{A}') (\\cate{K}F); \\cate{K}^-(\\mathcal{A}) → \\cate{D}^-(\\mathcal{A}) (Q); \\cate{K}^-(\\mathcal{A}') → \\cate{D}^-(\\mathcal{A}'). (Q'); \\cate{D}^-(\\mathcal{A}) → \\cate{D}^-(\\mathcal{A}'). (\\mathrm{L}F); \\cate{D}^-(\\mathcal{A}) ⇒ \\cate{K}^-…",
        "diagram_id": "chapter4-unit-048-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter4-unit-048.tex:134; tikzcd mandiri",
        "unit_filename": "chapter4-unit-048.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter4.overview"
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      "unit_links": [
        {
          "title": "Kategori Bertriangulasi dan Kategori Turunan",
          "unit_id": "o014.aljabr2.chapter4.overview",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-048"
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    {
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: FT → F'T (\\varphi T); FT → T'F (\\sim); F'T → T'F'. (\\sim); T'F → T'F'. (T'\\varphi).",
        "diagram_id": "chapter4-unit-049-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter4-unit-049.tex:56; tikzcd mandiri",
        "unit_filename": "chapter4-unit-049.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter4.triangulated-category-definition"
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      "unit_links": [
        {
          "title": "Definisi Kategori Bertriangulasi",
          "unit_id": "o014.aljabr2.chapter4.triangulated-category-definition",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter4-unit-049"
        }
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        "local_order": "1",
        "provenance": "id-ID/chapter6-unit-082.tex:122; tikzcd mandiri",
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        "local_order": "3",
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        "diagram_id": "chapter6-unit-082-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter6-unit-082.tex:251; tikzcd mandiri",
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        "alt_text_id": "Diagram kategori: \\cup: C^{p_1}(G, M_1) \\otimes C^{p_2}(G, M_2) → C^{p_1 + p_2}(G, M_1 \\otimes M_2); f_1 \\otimes f_2 → f_1(g_1, \\ldots, g_{p_1}) \\otimes (g_1 \\cdots g_{p_1} f_2(g_{p_1 + 1},….",
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        "local_order": "6",
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        "local_order": "7",
        "provenance": "id-ID/chapter6-unit-082.tex:426; tikzcd mandiri",
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      "native": {
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        "local_order": "8",
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        "diagram_id": "chapter6-unit-082-d009",
        "local_order": "9",
        "provenance": "id-ID/chapter6-unit-082.tex:603; tikzcd mandiri",
        "unit_filename": "chapter6-unit-082.tex"
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      "related_native": {},
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        "local_order": "10",
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        "local_order": "11",
        "provenance": "id-ID/chapter6-unit-082.tex:649; tikzcd mandiri",
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        "local_order": "12",
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        "diagram_id": "chapter6-unit-082-d013",
        "local_order": "13",
        "provenance": "id-ID/chapter6-unit-082.tex:761; tikzcd mandiri",
        "unit_filename": "chapter6-unit-082.tex"
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        "local_order": "1",
        "provenance": "id-ID/chapter6-unit-083.tex:78; tikzcd mandiri",
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        "local_order": "2",
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        "alt_text_id": "Diagram eksak: \\Ker(N_1) → \\Ker(N_2); \\Ker(N_2) → \\Ker(N_3); \\Ker(N_3) → \\Coker(N_1) (\\delta^{-1}); \\Coker(N_1) → \\Coker(N_2); \\Coker(N_2) → \\Coker(N_3); \\TaHm^{-1}(G, M') → \\Ker(N_1); \\TaHm^{-1}(G, M) → \\Ker(N_2); \\TaHm^{-1}(G, M'') → \\Ker(N_3); serta 3 panah lain.",
        "diagram_id": "chapter6-unit-083-d003",
        "local_order": "3",
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        "alt_text_id": "Diagram komutatif: \\Ind^G_H(N)_G → \\Ind^G_H(N)^G (\\nu^G); \\Ind^G_H(N)^G → N^H (\\sim); N_H → \\Ind^G_H(N)_G (\\sim); N_H → N^H (\\nu^H).",
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        "local_order": "4",
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      "kind": "diagrams",
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        "alt_text_id": "Diagram kategori: \\cdots → 0; 0 → 0; 0 → I^{0, G}; I^{0, G} → I^{1, G}; I^{1, G} → I^{2, G}; I^{2, G} → \\cdots; \\cdots → P_{2, G}; P_{2, G} → P_{1, G}; serta 8 panah lain.",
        "diagram_id": "chapter6-unit-083-d005",
        "local_order": "5",
        "provenance": "id-ID/chapter6-unit-083.tex:240; tikzcd mandiri",
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        "alt_text_id": "Diagram eksak: \\TaHm^{\\text{genap}}(C_m, A') → \\TaHm^{\\text{genap}}(C_m, A) (f_1); \\TaHm^{\\text{genap}}(C_m, A) → \\TaHm^{\\text{genap}}(C_m, A'') . (f_2); \\Hm^{\\text{ganjil}}(C_m, A'') → \\TaHm^{\\text{genap}}(C_m, A') (f_6); \\TaHm^{\\text{genap}}(C_m, A'') . → \\TaHm^{\\text{ganjil}}(C_m, A') (f_3); \\Ta…",
        "diagram_id": "chapter6-unit-083-d006",
        "local_order": "6",
        "provenance": "id-ID/chapter6-unit-083.tex:313; tikzcd mandiri",
        "unit_filename": "chapter6-unit-083.tex"
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        {
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        "diagram_id": "chapter6-unit-083-d007",
        "local_order": "7",
        "provenance": "id-ID/chapter6-unit-083.tex:363; tikzpicture mandiri",
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      "kind": "diagrams",
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        "alt_text_id": "Diagram kategori: \\mathrm{Infl}^G_{G/K}:G/K\\dcate{Mod} → G\\dcate{Mod}^\\infty:(\\cdot)^K; G\\dcate{Mod}^\\infty:(\\cdot)^K → \\mathrm{Infl}^G_{G/K}:G/K\\dcate{Mod}; \\Hom_G(\\mathrm{Infl}^G_{G/K}(M'),M) → \\Hom_{G/K}(M',M^K)..",
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        "local_order": "1",
        "provenance": "id-ID/chapter6-unit-084.tex:134; tikzcd mandiri",
        "unit_filename": "chapter6-unit-084.tex"
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        "o014.aljabr2.chapter6.profinite-cohomology-a"
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        "local_order": "1",
        "provenance": "id-ID/chapter6-unit-085.tex:244; tikzcd mandiri",
        "unit_filename": "chapter6-unit-085.tex"
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram eksak: 1 → \\Hm^0(G, A); \\Hm^0(G, A) → \\Hm^0(G, B) (\\Hm^0(u)); \\Hm^0(G, B) → \\Hm^0(G, C) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshif… (\\Hm^0(v)); \\Hm^0(G, C) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshif… → \\Hm^1(G, A) (\\delta^0); \\Hm^1(G, A) → \\Hm^1(G, B). (\\Hm…",
        "diagram_id": "chapter6-unit-086-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter6-unit-086.tex:321; tikzcd mandiri",
        "unit_filename": "chapter6-unit-086.tex"
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          "description_id": "Barisan eksak dalam himpunan bertitik: 1 → H^0(G,A) → H^0(G,B) → H^0(G,C) → H^1(G,A) → H^1(G,B). Panah berlabel berturut-turut H^0(u), H^0(v), δ^0, dan H^1(u).",
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      "native": {
        "alt_text_id": "Diagram kategori: 1 → \\Hm^0(G, A); \\Hm^0(G, A) → \\Hm^0(G, B) (\\Hm^0(u)); \\Hm^0(G, B) → \\Hm^0(G, C) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshif… (\\Hm^0(v)); \\Hm^0(G, C) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshif… → \\Hm^1(G, A) (\\delta^0); \\Hm^1(G, A) → \\Hm^1(G, B) (\\…",
        "diagram_id": "chapter6-unit-086-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter6-unit-086.tex:335; tikzcd mandiri",
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        "reader_override": {
          "description_id": "Barisan eksak dalam himpunan bertitik: 1 → H^0(G,A) → H^0(G,B) → H^0(G,C) → H^1(G,A) → H^1(G,B) → H^1(G,C). Panah penghubung H^0(G,C) → H^1(G,A) berlabel δ^0.",
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      "native": {
        "alt_text_id": "Diagram eksak: 1 → \\Hm^0(G, A); \\Hm^0(G, A) → \\Hm^0(G, B) (\\Hm^0(u)); \\Hm^0(G, B) → \\Hm^0(G, C) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshif… (\\Hm^0(v)); \\Hm^0(G, C) \\tikztostart.east) |- (A) [near end]\\tikztonodes -| ([xshif… → \\Hm^1(G, A) (\\delta^0); \\Hm^1(G, A) → \\Hm^1(G, B) (\\Hm^…",
        "diagram_id": "chapter6-unit-086-d003",
        "local_order": "3",
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        "reader_override": {
          "description_id": "Barisan eksak: 1 → H^0(G,A) → H^0(G,B) → H^0(G,C) → H^1(G,A) → H^1(G,B) → H^1(G,C) → H^2(G,A). Panah penghubung berlabel δ^0 dan δ^1; panah lainnya diinduksi oleh u dan v.",
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        "diagram_id": "chapter6-unit-087-d001",
        "local_order": "1",
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      "native": {
        "alt_text_id": "Diagram komutatif: \\Hm^1(G,{}^cA) → \\Hm^1(G,{}^cB); \\Hm^1(G,{}^cA) → \\Hm^1(G,A) ({\\bm\\nu}_c); \\Hm^1(G,{}^cB) → \\Hm^1(G,B). (\\bm{\\nu}_c); \\Hm^1(G,A) → \\Hm^1(G,B)..",
        "diagram_id": "chapter6-unit-087-d002",
        "local_order": "2",
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        "local_order": "1",
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        "alt_text_id": "Diagram komutatif: \\munit \\otimes A → A \\otimes A (\\eta \\otimes \\identity); \\munit \\otimes A → A (\\sim); A \\otimes A → A (\\mu); A \\otimes \\munit → A \\otimes A (\\identity \\otimes \\eta); A \\otimes \\munit → A (\\sim).",
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        "local_order": "2",
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        "local_order": "15",
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        "diagram_id": "chapter7-unit-096-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter7-unit-096.tex:78; tikzcd mandiri",
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        "o014.aljabr2.chapter7.morita-theory-a"
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          "title": "Teori Morita",
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter7-unit-096"
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        "diagram_id": "chapter7-unit-096-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter7-unit-096.tex:225; tikzcd mandiri; label=eqn:AB-adjunction",
        "unit_filename": "chapter7-unit-096.tex"
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      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter7.morita-theory-a"
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        "diagram_id": "chapter7-unit-097-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter7-unit-097.tex:96; tikzcd mandiri; label=eqn:AB-adjunction-2",
        "unit_filename": "chapter7-unit-097.tex"
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        "o014.aljabr2.chapter7.morita-theory-b"
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        "local_order": "2",
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        "local_order": "3",
        "provenance": "id-ID/chapter7-unit-097.tex:112; tikzcd mandiri",
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        "diagram_id": "chapter7-unit-097-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter7-unit-097.tex:125; tikzcd mandiri",
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        "diagram_id": "chapter7-unit-097-d005",
        "local_order": "5",
        "provenance": "id-ID/chapter7-unit-097.tex:248; tikzcd mandiri",
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        "local_order": "1",
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        "diagram_id": "chapter7-unit-099-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter7-unit-099.tex:162; tikzcd mandiri",
        "unit_filename": "chapter7-unit-099.tex"
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        "diagram_id": "chapter7-unit-099-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter7-unit-099.tex:170; tikzcd mandiri",
        "unit_filename": "chapter7-unit-099.tex"
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        "local_order": "2",
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        "diagram_id": "chapter8-unit-106-d001",
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        "alt_text_id": "Diagram komutatif: {[m]^{\\opp}} → {[n]^{\\opp}} (f^{\\opp}); {[m]} → {[n]} (\\text{monoton); {[m]} → {[m]^{\\opp}} (\\sim); {[n]} → {[n]^{\\opp}} (\\sim).",
        "diagram_id": "chapter8-unit-106-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter8-unit-106.tex:371; tikzcd mandiri",
        "unit_filename": "chapter8-unit-106.tex"
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        "diagram_id": "chapter8-unit-107-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter8-unit-107.tex:96; tikzcd mandiri",
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      "related_native": {},
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        "provenance": "id-ID/chapter8-unit-108.tex:136; tikzcd mandiri",
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        "diagram_id": "chapter8-unit-108-d002",
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        "diagram_id": "chapter8-unit-108-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter8-unit-108.tex:148; tikzcd mandiri",
        "unit_filename": "chapter8-unit-108.tex"
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      "related_native": {},
      "unit_ids": [
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      "unit_links": [
        {
          "title": "Contoh: Saraf Kategori",
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        "local_order": "4",
        "provenance": "id-ID/chapter8-unit-108.tex:156; tikzcd mandiri",
        "unit_filename": "chapter8-unit-108.tex"
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      "related_native": {},
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        {
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-108"
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        "provenance": "id-ID/chapter8-unit-108.tex:159; tikzcd mandiri",
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      "related_native": {},
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        "local_order": "6",
        "provenance": "id-ID/chapter8-unit-108.tex:162; tikzcd mandiri",
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      "related_native": {},
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      "unit_links": [
        {
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    {
      "discovery_scope": "exact_target_file",
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      "native": {
        "alt_text_id": "Diagram kategori: 1 → 3. (hg); 0 → 1 (f); 0 → 3. (h(gf)).",
        "diagram_id": "chapter8-unit-108-d007",
        "local_order": "7",
        "provenance": "id-ID/chapter8-unit-108.tex:169; tikzcd mandiri",
        "unit_filename": "chapter8-unit-108.tex"
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      "related_native": {},
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      "native": {
        "alt_text_id": "Diagram komutatif: \\Hom(\\Delta^n, X) → \\Hom(\\Lambda^n_i, X); \\Hom(\\Delta^n, X) → \\Hom(\\Delta^n, \\mathrm{N}\\mathcal{C}); \\Hom(\\Delta^n, \\mathrm{N}\\mathcal{C}) → \\Hom(\\Lambda^n_i, \\mathrm{N}\\mathcal{C}).; \\Hom(\\Lambda^n_i, X) → \\Hom(\\Lambda^n_i, \\mathrm{N}\\mathcal{C})..",
        "diagram_id": "chapter8-unit-108-d008",
        "local_order": "8",
        "provenance": "id-ID/chapter8-unit-108.tex:183; tikzcd mandiri",
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        {
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-108"
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      "discovery_scope": "exact_target_file",
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        "alt_text_id": "Diagram TikZ dengan label atau simpul e_0, e_1, e_2, n=2, (kasus khusus $n=2$); 3 untai, sisi, atau panah digambar menurut komposisi. Konteks: |\\Delta^n| := \\left\\{ (x_0, \\ldots, x_n) \\in (\\R_{\\geq 0})^{n+1} : \\sum_{i=0}^n x_i = 1 \\right\\} \\quad",
        "diagram_id": "chapter8-unit-109-d001",
        "local_order": "1",
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        "diagram_id": "chapter8-unit-109-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter8-unit-109.tex:37; tikzcd mandiri",
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      "related_native": {},
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-109"
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        "diagram_id": "chapter8-unit-109-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter8-unit-109.tex:49; tikzpicture mandiri",
        "unit_filename": "chapter8-unit-109.tex"
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      "related_native": {},
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        "diagram_id": "chapter8-unit-109-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter8-unit-109.tex:107; tikzcd mandiri",
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      "related_native": {},
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        {
          "title": "Funktor Realisasi Geometris",
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        "diagram_id": "chapter8-unit-109-d005",
        "local_order": "5",
        "provenance": "id-ID/chapter8-unit-109.tex:148; tikzcd mandiri",
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      "native": {
        "alt_text_id": "Diagram TikZ dengan label atau simpul 1, 3, 2, (O)!0.15!(C), 0, (A) + (-1.5, -0.2), |\\Lambda^3_0| =, $|\\Lambda^3_0| =$; 1 untai, sisi, atau panah digambar menurut komposisi. Konteks: sudut ke-$k$. Berikut salah satu ilustrasinya:",
        "diagram_id": "chapter8-unit-109-d006",
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      "related_native": {},
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        "o014.aljabr2.chapter8.geometric-realization"
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-109"
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        "alt_text_id": "Diagram TikZ dengan label atau simpul \\mathcal{X}, X; 7 untai, sisi, atau panah digambar menurut komposisi. Konteks: titik. Secara visual,",
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      "native": {
        "alt_text_id": "Diagram kategori: \\Hom_{\\cate{Top}}(|X|, E) ⇒ \\Hom_{\\cate{sSet}}(X, \\mathrm{Sing}(E)) (1:1); \\varphi → {\\left[ X_n \\xrightarrow{x \\mapsto \\varphi \\circ i_{n, x}} \\Hom_{\\cate{…; \\psi = {\\left[ \\psi_n: X_n \\to \\Hom_{\\cate{Top}}(|\\Delta^n|, E) \\right]… → \\displaystyle\\varinjlim_{(n, x)} \\left( |\\Delta…",
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        "local_order": "8",
        "provenance": "id-ID/chapter8-unit-109.tex:281; tikzcd mandiri",
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      "related_native": {},
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-109"
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      "native": {
        "alt_text_id": "Diagram kategori: \\cate{sSet} → \\cate{CGHaus} (|\\cdot|); \\cate{CGHaus} → \\cate{Top} . (\\text{funktor inklusi); \\cate{CGHaus} → \\cate{sSet} (\\mathrm{Sing); \\cate{Top} . → \\cate{CGHaus} (k).",
        "diagram_id": "chapter8-unit-109-d009",
        "local_order": "9",
        "provenance": "id-ID/chapter8-unit-109.tex:322; tikzcd mandiri",
        "unit_filename": "chapter8-unit-109.tex"
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      "related_native": {},
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-109"
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        "alt_text_id": "Diagram komutatif: X \\times \\Delta^0 → X \\times \\Delta^1 (\\identity_X \\times \\mathrm{d}^0); X \\times \\Delta^0 → X (\\sim); X → Y (f); X \\times \\Delta^1 → Y (H); X \\times \\Delta^0 → X \\times \\Delta^1 (\\identity_X \\times \\mathrm{d}^1); X → Y (g).",
        "diagram_id": "chapter8-unit-109-d010",
        "local_order": "10",
        "provenance": "id-ID/chapter8-unit-109.tex:376; tikzcd mandiri",
        "unit_filename": "chapter8-unit-109.tex"
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      "related_native": {},
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        "alt_text_id": "Diagram TikZ dengan label atau simpul i=0, (p, q), $i=0$; 2 untai, sisi, atau panah digambar menurut komposisi. Konteks: $i=0,\\ldots,n$. Jika $n=p+q$, keadaan ini dapat digambarkan sebagai berikut:",
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      "related_native": {},
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        "o014.aljabr2.chapter8.geometric-realization"
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        {
          "title": "Funktor Realisasi Geometris",
          "unit_id": "o014.aljabr2.chapter8.geometric-realization",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-109"
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      "discovery_scope": "exact_target_file",
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      "kind": "diagrams",
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        "alt_text_id": "Diagram TikZ dengan label atau simpul (A) + (0, -3), (B) + (0, -3), (C) + (0, -3), (A) + (-5, -0.3), (B) + (-5, -0.3), (Q) + (-5, -0.3), (R) + (-5, -0.3), (P) + (-5, -0.3), (C) + (-5, -0.3), (B)!0.5!(Q) + (-4.5, -0.5), serta 9 label lain; 12 untai, sisi, atau panah digambar menurut komposisi. Konte…",
        "diagram_id": "chapter8-unit-109-d012",
        "local_order": "12",
        "provenance": "id-ID/chapter8-unit-109.tex:484; tikzpicture mandiri",
        "unit_filename": "chapter8-unit-109.tex"
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      "related_native": {},
      "unit_ids": [
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-109"
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      "discovery_scope": "exact_target_file",
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        "alt_text_id": "Diagram kategori: \\cate{Ch}_{\\geq 0}(\\mathcal{A}) → \\cate{s}\\mathcal{A} (\\Gamma); \\cate{s}\\mathcal{A} → \\cate{Ch}_{\\geq 0}(\\mathcal{A}) (\\mathrm{N}); \\cate{s}\\mathcal{A} → \\cate{Ch}_{\\geq 0}(\\mathcal{A}) (\\mathrm{C}).",
        "diagram_id": "chapter8-unit-110-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter8-unit-110.tex:34; tikzcd mandiri",
        "unit_filename": "chapter8-unit-110.tex"
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          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-110"
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        "diagram_id": "chapter8-unit-110-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter8-unit-110.tex:142; tikzcd mandiri; label=eqn:Dold-Kan-epi-mono",
        "unit_filename": "chapter8-unit-110.tex"
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      "related_native": {},
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        {
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          "unit_id": "o014.aljabr2.chapter8.dold-kan-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-110"
        }
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    {
      "discovery_scope": "exact_target_file",
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: {[n]} ↠ {[k]} (t); {[n-1]} → {[n]} (\\mathrm{d}^i); {[n-1]} ↠ {[k]} (t\\mathrm{d}^i); {[k]} → {[k]} (\\identity).",
        "diagram_id": "chapter8-unit-110-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter8-unit-110.tex:222; tikzcd mandiri",
        "unit_filename": "chapter8-unit-110.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.dold-kan-a"
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      "unit_links": [
        {
          "title": "Korespondensi Dold–Kan",
          "unit_id": "o014.aljabr2.chapter8.dold-kan-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-110"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-110-d004",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\Gamma: \\cate{Ch}_{\\geq 0}(\\mathcal{A}) → \\cate{s}\\mathcal{A} : \\mathrm{N} .; \\cate{s}\\mathcal{A} : \\mathrm{N} . → \\Gamma: \\cate{Ch}_{\\geq 0}(\\mathcal{A}).",
        "diagram_id": "chapter8-unit-110-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter8-unit-110.tex:240; tikzcd mandiri",
        "unit_filename": "chapter8-unit-110.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.dold-kan-a"
      ],
      "unit_links": [
        {
          "title": "Korespondensi Dold–Kan",
          "unit_id": "o014.aljabr2.chapter8.dold-kan-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-110"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-110-d005",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: A_k → (\\mathrm{N}X)_k (\\phi_k); A_k → A_l (\\Phi_{u, t}); (\\mathrm{N}X)_k ↪ X_k; (\\mathrm{N}X)_k → (\\mathrm{N}X)_l (v^*|_{(\\mathrm{N}X)_k}); X_k → X_n (t^*); X_k → X_l (v^*); X_n → X_m. (f^*); A_l → (\\mathrm{N}X)_l (\\phi_l); serta 2 panah lain.",
        "diagram_id": "chapter8-unit-110-d005",
        "local_order": "5",
        "provenance": "id-ID/chapter8-unit-110.tex:275; tikzcd mandiri",
        "unit_filename": "chapter8-unit-110.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.dold-kan-a"
      ],
      "unit_links": [
        {
          "title": "Korespondensi Dold–Kan",
          "unit_id": "o014.aljabr2.chapter8.dold-kan-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-110"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-111-d001",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\cate{Ch}_{\\geq 0}(\\mathcal{A}) → \\cate{Ch}_{\\geq 0}(\\tilde{\\mathcal{A}}^\\wedge) (\\tilde{h}_{\\mathcal{A}}); \\cate{Ch}_{\\geq 0}(\\mathcal{A}) → \\cate{s}\\mathcal{A} (\\Gamma); \\cate{s}\\mathcal{A} → \\cate{s}\\tilde{\\mathcal{A}}^\\wedge. (\\tilde{h}_{\\mathcal{A}}); \\cate{Ch}_{\\geq 0}(\\tild…",
        "diagram_id": "chapter8-unit-111-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter8-unit-111.tex:54; tikzcd mandiri",
        "unit_filename": "chapter8-unit-111.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.dold-kan-b"
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      "unit_links": [
        {
          "title": "Dold Kan B",
          "unit_id": "o014.aljabr2.chapter8.dold-kan-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-111"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-111-d002",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: \\bigoplus_{0 \\leq i < n} X_{n-1} → X_n (\\Psi_n); X_j ↪ \\bigoplus_{0 \\leq i < n} X_{n-1} (\\text{suku langsung); X_j → X_n (s_j).",
        "diagram_id": "chapter8-unit-111-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter8-unit-111.tex:117; tikzcd mandiri",
        "unit_filename": "chapter8-unit-111.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.dold-kan-b"
      ],
      "unit_links": [
        {
          "title": "Dold Kan B",
          "unit_id": "o014.aljabr2.chapter8.dold-kan-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-111"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-111-d003",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: (\\Gamma A)_n → (\\Gamma A)_{n-1} (\\sum_i (-1)^i d^{\\Gamma A}_i); (\\Gamma A)_n → A_n (\\text{proyeksi); (\\Gamma A)_{n-1} → A_{n-1} (\\text{proyeksi); A_n → A_{n-1} (\\partial^A_n); A_n → (\\mathrm{N}\\Gamma A)_n (\\eta); A_{n-1} → (\\mathrm{N}\\Gamma A)_{n-1}. (\\eta); (\\mathrm{N}\\Gamma A)_…",
        "diagram_id": "chapter8-unit-111-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter8-unit-111.tex:170; tikzcd mandiri",
        "unit_filename": "chapter8-unit-111.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.dold-kan-b"
      ],
      "unit_links": [
        {
          "title": "Dold Kan B",
          "unit_id": "o014.aljabr2.chapter8.dold-kan-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-111"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
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      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: F : \\mathcal{C} → \\mathcal{D}: G; \\mathcal{D}: G → F : \\mathcal{C}.",
        "diagram_id": "chapter8-unit-113-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter8-unit-113.tex:73; tikzcd mandiri",
        "unit_filename": "chapter8-unit-113.tex"
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      "related_native": {},
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        {
          "title": "Konstruksi bar",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-113"
        }
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    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-113-d002",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: B \\dotimes{A} (\\cdot): A\\dcate{Mod} → B\\dcate{Mod}: \\text{lupa}; B\\dcate{Mod}: \\text{lupa} → B \\dotimes{A} (\\cdot): A\\dcate{Mod}.",
        "diagram_id": "chapter8-unit-113-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter8-unit-113.tex:147; tikzcd mandiri",
        "unit_filename": "chapter8-unit-113.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bar-construction-a"
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        {
          "title": "Konstruksi bar",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-113"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
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      "id": "chapter8-unit-113-d003",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\mathrm{Free}^T : \\mathcal{C} → \\mathcal{C}^T: U^T (\\text{bebas); \\mathcal{C}^T: U^T → \\mathrm{Free}^T : \\mathcal{C} (\\text{lupa).",
        "diagram_id": "chapter8-unit-113-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter8-unit-113.tex:162; tikzcd mandiri",
        "unit_filename": "chapter8-unit-113.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bar-construction-a"
      ],
      "unit_links": [
        {
          "title": "Konstruksi bar",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-113"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-113-d004",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: \\cdots → T^3 M (\\mu_{T^2 M}); \\cdots → T^3 M; \\cdots → T^3 M (T^3 a); T^3 M → T^2 M (\\mu_{TM); T^3 M → T^2 M (T\\mu_M); T^3 M → T^2 M (T^2 a); T^2 M → TM (\\mu_M); T^2 M → TM (Ta); serta 1 panah lain.",
        "diagram_id": "chapter8-unit-113-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter8-unit-113.tex:211; tikzcd mandiri",
        "unit_filename": "chapter8-unit-113.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bar-construction-a"
      ],
      "unit_links": [
        {
          "title": "Konstruksi bar",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-113"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-114-d001",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: F : \\mathcal{C} → \\mathcal{D}: G; \\mathcal{D}: G → F : \\mathcal{C}.",
        "diagram_id": "chapter8-unit-114-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter8-unit-114.tex:51; tikzcd mandiri",
        "unit_filename": "chapter8-unit-114.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bar-construction-b"
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      "unit_links": [
        {
          "title": "Bar Construction B",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-114"
        }
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    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-114-d002",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: T^{n+1} G → T^{n+2}G (k_n = \\eta T^{n+1}G); T^{n+1} G → T^n G (d_{i-1} = \\varphi); T^{n+2}G → T^{n+1} G (d_i = T\\varphi); T^n G → T^{n+1} G (k_{n-1} = \\eta T^n G).",
        "diagram_id": "chapter8-unit-114-d002",
        "local_order": "2",
        "provenance": "id-ID/chapter8-unit-114.tex:86; tikzcd mandiri",
        "unit_filename": "chapter8-unit-114.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bar-construction-b"
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        {
          "title": "Bar Construction B",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-114"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-114-d003",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: F : \\mathcal{A} → \\mathcal{B}: G; \\mathcal{B}: G → F : \\mathcal{A}.",
        "diagram_id": "chapter8-unit-114-d003",
        "local_order": "3",
        "provenance": "id-ID/chapter8-unit-114.tex:120; tikzcd mandiri",
        "unit_filename": "chapter8-unit-114.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bar-construction-b"
      ],
      "unit_links": [
        {
          "title": "Bar Construction B",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-114"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-114-d004",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: R \\otimes (\\cdot): \\Bbbk\\dcate{Mod} → R\\dcate{Mod}: \\text{lupa}; R\\dcate{Mod}: \\text{lupa} → R \\otimes (\\cdot): \\Bbbk\\dcate{Mod}.",
        "diagram_id": "chapter8-unit-114-d004",
        "local_order": "4",
        "provenance": "id-ID/chapter8-unit-114.tex:196; tikzcd mandiri",
        "unit_filename": "chapter8-unit-114.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bar-construction-b"
      ],
      "unit_links": [
        {
          "title": "Bar Construction B",
          "unit_id": "o014.aljabr2.chapter8.bar-construction-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-114"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-115-d001",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram kategori: (\\tot X)_n → (\\tot X)_{n-1} (\\partial_n); X_{p,q} ↪ (\\tot X)_n; X_{p,q} → X_{p-1, q} \\oplus X_{p, q-1} . ((\\phori_{p, q}, \\; (-1)^p \\pvert_{p, q})); X_{p-1, q} \\oplus X_{p, q-1} . ↪ (\\tot X)_{n-1}.",
        "diagram_id": "chapter8-unit-115-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter8-unit-115.tex:177; tikzcd mandiri",
        "unit_filename": "chapter8-unit-115.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bisimplicial-a"
      ],
      "unit_links": [
        {
          "title": "Objek bisimplisial",
          "unit_id": "o014.aljabr2.chapter8.bisimplicial-a",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-115"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
      "flags": [],
      "id": "chapter8-unit-116-d001",
      "kind": "diagrams",
      "native": {
        "alt_text_id": "Diagram komutatif: \\mathrm{C}A \\otimes \\mathrm{C}B → \\mathrm{C}(A \\otimes B) (\\overline{\\mathrm{EZ}}); \\mathrm{C}A \\otimes \\mathrm{C}B ↠ \\mathrm{N}A \\otimes \\mathrm{N}B; \\mathrm{C}(A \\otimes B) → \\mathrm{C}A \\otimes \\mathrm{C}B (\\overline{\\mathrm{AW}}); \\mathrm{C}(A \\otimes B) ↠ \\mathrm{N}(A \\otime…",
        "diagram_id": "chapter8-unit-116-d001",
        "local_order": "1",
        "provenance": "id-ID/chapter8-unit-116.tex:89; tikzcd mandiri",
        "unit_filename": "chapter8-unit-116.tex"
      },
      "related_native": {},
      "unit_ids": [
        "o014.aljabr2.chapter8.bisimplicial-b"
      ],
      "unit_links": [
        {
          "title": "Bisimplicial B",
          "unit_id": "o014.aljabr2.chapter8.bisimplicial-b",
          "url": "https://kokunoyumeto.github.io/metode-aljabar-jilid-2-id/#unit-chapter8-unit-116"
        }
      ]
    },
    {
      "discovery_scope": "exact_target_file",
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      "id": "o014.aljabr2.chapter1.linear-categories-over-commutative-rings",
      "sequence": 12,
      "title": "Perumuman: Kategori Linear atas Gelanggang Komutatif"
    },
    {
      "id": "o014.aljabr2.chapter1.limits-through-functors",
      "sequence": 13,
      "title": "Meninjau Limit melalui Funktor"
    },
    {
      "id": "o014.aljabr2.chapter1.filtered-inductive-limits",
      "sequence": 14,
      "title": "Limit Induktif Terfilter"
    },
    {
      "id": "o014.aljabr2.chapter1.kan-extensions",
      "sequence": 15,
      "title": "Ekstensi Kan"
    },
    {
      "id": "o014.aljabr2.chapter1.kan-extensions-as-limits",
      "sequence": 16,
      "title": "Konstruksi Ekstensi Kan melalui Limit"
    },
    {
      "id": "o014.aljabr2.chapter1.gabriel-zisman-localization",
      "sequence": 17,
      "title": "Lokalisasi Gabriel--Zisman"
    },
    {
      "id": "o014.aljabr2.chapter1.kan-extensions-along-localization",
      "sequence": 18,
      "title": "Ekstensi Kan sepanjang Lokalisasi"
    },
    {
      "id": "o014.aljabr2.chapter1.adjoint-functor-theorem",
      "sequence": 19,
      "title": "Teorema Funktor Adjoin"
    },
    {
      "id": "o014.aljabr2.chapter2.overview",
      "sequence": 20,
      "title": "Kategori Abelian"
    },
    {
      "id": "o014.aljabr2.chapter2.abelian-category-definition",
      "sequence": 21,
      "title": "Definisi Kategori Abelian"
    },
    {
      "id": "o014.aljabr2.chapter2.first-look-at-complexes",
      "sequence": 22,
      "title": "Mengenal Kompleks"
    },
    {
      "id": "o014.aljabr2.chapter2.diagram-lemmas",
      "sequence": 23,
      "title": "Beberapa Lema Diagram"
    },
    {
      "id": "o014.aljabr2.chapter2.glimpse-of-lattice-theory",
      "sequence": 24,
      "title": "Sekilas tentang Teori Kisi"
    },
    {
      "id": "o014.aljabr2.chapter2.direct-sum-decomposition",
      "sequence": 25,
      "title": "Dekomposisi Jumlah Langsung"
    },
    {
      "id": "o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems",
      "sequence": 26,
      "title": "Subobjek dan Teorema Isomorfisme"
    },
    {
      "id": "o014.aljabr2.chapter2.simplicity-and-semisimplicity",
      "sequence": 27,
      "title": "Objek Sederhana dan Semisederhana"
    },
    {
      "id": "o014.aljabr2.chapter2.exact-functors-injective-projective-objects",
      "sequence": 28,
      "title": "Funktor Eksak, Objek Injektif, dan Projektif"
    },
    {
      "id": "o014.aljabr2.chapter2.serre-subcategories-and-k0-groups",
      "sequence": 29,
      "title": "Subkategori Serre dan Grup K0"
    },
    {
      "id": "o014.aljabr2.chapter2.grothendieck-categories",
      "sequence": 30,
      "title": "Kategori Grothendieck"
    },
    {
      "id": "o014.aljabr2.chapter3.overview",
      "sequence": 31,
      "title": "Kompleks"
    },
    {
      "id": "o014.aljabr2.chapter3.complexes-over-additive-categories",
      "sequence": 32,
      "title": "Kompleks pada Kategori Aditif"
    },
    {
      "id": "o014.aljabr2.chapter3.hom-complex-and-homotopy",
      "sequence": 33,
      "title": "Kompleks Hom dan Homotopi"
    },
    {
      "id": "o014.aljabr2.chapter3.mapping-cone",
      "sequence": 34,
      "title": "Kerucut pemetaan"
    },
    {
      "id": "o014.aljabr2.chapter3.opposite-category-complexes",
      "sequence": 35,
      "title": "Kompleks pada kategori lawan"
    },
    {
      "id": "o014.aljabr2.chapter3.double-complexes",
      "sequence": 36,
      "title": "Bikompleks"
    },
    {
      "id": "o014.aljabr2.chapter3.abelian-category-complexes",
      "sequence": 37,
      "title": "Kompleks pada kategori abelian"
    },
    {
      "id": "o014.aljabr2.chapter3.mapping-cone-and-long-exact-sequences",
      "sequence": 38,
      "title": "Kerucut pemetaan: barisan eksak panjang"
    },
    {
      "id": "o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology",
      "sequence": 39,
      "title": "Latihan: Homologi dan Kohomologi Hochschild"
    },
    {
      "id": "o014.aljabr2.chapter3.truncation-functors",
      "sequence": 40,
      "title": "Funktor pemenggalan"
    },
    {
      "id": "o014.aljabr2.chapter3.double-complex-cohomology",
      "sequence": 41,
      "title": "Kohomologi bikompleks"
    },
    {
      "id": "o014.aljabr2.chapter3.resolutions",
      "sequence": 42,
      "title": "Resolusi"
    },
    {
      "id": "o014.aljabr2.chapter3.classical-derived-functors",
      "sequence": 43,
      "title": "Funktor turunan klasik"
    },
    {
      "id": "o014.aljabr2.chapter3.example-lim1",
      "sequence": 44,
      "title": "Contoh: lim^1"
    },
    {
      "id": "o014.aljabr2.chapter3.ext-tor",
      "sequence": 45,
      "title": "Contoh: Ext dan Tor"
    },
    {
      "id": "o014.aljabr2.chapter3.k-injectives",
      "sequence": 46,
      "title": "Kompleks K-injektif dan K-projektif"
    },
    {
      "id": "o014.aljabr2.chapter3.exercises",
      "sequence": 47,
      "title": "Latihan"
    },
    {
      "id": "o014.aljabr2.chapter4.overview",
      "sequence": 48,
      "title": "Kategori Bertriangulasi dan Kategori Turunan"
    },
    {
      "id": "o014.aljabr2.chapter4.triangulated-category-definition",
      "sequence": 49,
      "title": "Definisi Kategori Bertriangulasi"
    },
    {
      "id": "o014.aljabr2.chapter4.cohomological-functors",
      "sequence": 50,
      "title": "Funktor Kohomologis dan Barisan Eksak Panjang"
    },
    {
      "id": "o014.aljabr2.chapter4.triangulated-basics",
      "sequence": 51,
      "title": "Sifat-Sifat Dasar Kategori Bertriangulasi"
    },
    {
      "id": "o014.aljabr2.chapter4.triangulated-localization",
      "sequence": 52,
      "title": "Lokalisasi Kategori Bertriangulasi"
    },
    {
      "id": "o014.aljabr2.chapter4.verdier-localization",
      "sequence": 53,
      "title": "Verdier Localization"
    },
    {
      "id": "o014.aljabr2.chapter4.derived-categories",
      "sequence": 54,
      "title": "Kategori Turunan"
    },
    {
      "id": "o014.aljabr2.chapter4.morphisms-extensions",
      "sequence": 55,
      "title": "Morfisme dan Ekstensi"
    },
    {
      "id": "o014.aljabr2.chapter4.triangulated-functor-localization",
      "sequence": 56,
      "title": "Funktor Bertriangulasi dan Lokalisasi"
    },
    {
      "id": "o014.aljabr2.chapter4.derived-functors-general",
      "sequence": 57,
      "title": "Teori Umum Funktor Turunan"
    },
    {
      "id": "o014.aljabr2.chapter4.bounded-derived-functors",
      "sequence": 58,
      "title": "Funktor Turunan Terbatas"
    },
    {
      "id": "o014.aljabr2.chapter4.rhom",
      "sequence": 59,
      "title": "Contoh: RHom"
    },
    {
      "id": "o014.aljabr2.chapter4.rlim-homotopy-limit",
      "sequence": 60,
      "title": "Contoh: RRlim sebagai Limit Homotopi"
    },
    {
      "id": "o014.aljabr2.chapter4.unbounded-derived-functors",
      "sequence": 61,
      "title": "Funktor Turunan Tak Terbatas"
    },
    {
      "id": "o014.aljabr2.chapter4.k-flat-derived-tensor-a",
      "sequence": 62,
      "title": "Contoh: Kompleks K-Datar dan otimesL"
    },
    {
      "id": "o014.aljabr2.chapter4.k-flat-derived-tensor-b",
      "sequence": 63,
      "title": "Latihan"
    },
    {
      "id": "o014.aljabr2.chapter5.intro-filtration-grading",
      "sequence": 64,
      "title": "Barisan Spektral"
    },
    {
      "id": "o014.aljabr2.chapter5.general-spectral-sequences",
      "sequence": 65,
      "title": "Definisi umum barisan spektral"
    },
    {
      "id": "o014.aljabr2.chapter5.exact-couples",
      "sequence": 66,
      "title": "Pasangan eksak"
    },
    {
      "id": "o014.aljabr2.chapter5.filtered-differential-spectral-sequence",
      "sequence": 67,
      "title": "Barisan spektral objek diferensial terfiltrasi"
    },
    {
      "id": "o014.aljabr2.chapter5.filtered-complex-spectral-sequence",
      "sequence": 68,
      "title": "Barisan spektral kompleks terfiltrasi"
    },
    {
      "id": "o014.aljabr2.chapter5.bicomplex-spectral-sequences-applications",
      "sequence": 69,
      "title": "Barisan spektral bikompleks dan penerapannya"
    },
    {
      "id": "o014.aljabr2.chapter5.multiplicative-structures",
      "sequence": 70,
      "title": "Sekilas tentang struktur perkalian"
    },
    {
      "id": "o014.aljabr2.chapter5.exercises",
      "sequence": 71,
      "title": "Latihan"
    },
    {
      "id": "o014.aljabr2.chapter6.overview-g-modules-resolutions",
      "sequence": 72,
      "title": "Homologi dan Kohomologi Grup"
    },
    {
      "id": "o014.aljabr2.chapter6.group-homology-cohomology",
      "sequence": 73,
      "title": "Homologi dan Kohomologi Grup"
    },
    {
      "id": "o014.aljabr2.chapter6.low-degree-cohomology",
      "sequence": 74,
      "title": "Kohomologi berderajat rendah: homomorfisme silang dan ekstensi grup"
    },
    {
      "id": "o014.aljabr2.chapter6.induced-modules",
      "sequence": 75,
      "title": "Modul terinduksi"
    },
    {
      "id": "o014.aljabr2.chapter6.change-of-group",
      "sequence": 76,
      "title": "Perubahan grup"
    },
    {
      "id": "o014.aljabr2.chapter6.group-extensions-revisited",
      "sequence": 77,
      "title": "Meninjau kembali ekstensi grup"
    },
    {
      "id": "o014.aljabr2.chapter6.cyclic-and-free-groups",
      "sequence": 78,
      "title": "Contoh: grup siklik dan grup bebas"
    },
    {
      "id": "o014.aljabr2.chapter6.finite-index-subgroups",
      "sequence": 79,
      "title": "Subgrup Berindeks Hingga"
    },
    {
      "id": "o014.aljabr2.chapter6.lhs-spectral-sequence-a",
      "sequence": 80,
      "title": "Barisan spektral Lyndon–Hochschild–Serre"
    },
    {
      "id": "o014.aljabr2.chapter6.lhs-spectral-sequence-b",
      "sequence": 81,
      "title": "Lhs Spectral Sequence B"
    },
    {
      "id": "o014.aljabr2.chapter6.cup-product",
      "sequence": 82,
      "title": "Operasi Hasil Kali Cawan"
    },
    {
      "id": "o014.aljabr2.chapter6.tate-cohomology",
      "sequence": 83,
      "title": "Kohomologi Tate"
    },
    {
      "id": "o014.aljabr2.chapter6.profinite-cohomology-a",
      "sequence": 84,
      "title": "Kohomologi grup profinit"
    },
    {
      "id": "o014.aljabr2.chapter6.profinite-cohomology-b",
      "sequence": 85,
      "title": "Profinite Cohomology B"
    },
    {
      "id": "o014.aljabr2.chapter6.nonabelian-cohomology",
      "sequence": 86,
      "title": "Kohomologi Nonabelian"
    },
    {
      "id": "o014.aljabr2.chapter6.exercises",
      "sequence": 87,
      "title": "Latihan"
    },
    {
      "id": "o014.aljabr2.chapter7.monoidal-algebras",
      "sequence": 88,
      "title": "Teori Monad"
    },
    {
      "id": "o014.aljabr2.chapter7.differential-graded-structures",
      "sequence": 89,
      "title": "Contoh: Struktur Diferensial Bergradasi"
    },
    {
      "id": "o014.aljabr2.chapter7.closed-monoidal-categories",
      "sequence": 90,
      "title": "Kategori Monoidal Tertutup"
    },
    {
      "id": "o014.aljabr2.chapter7.closed-structure-dgcat",
      "sequence": 91,
      "title": "Studi Kasus: Struktur Tertutup pada Kategori-dg"
    },
    {
      "id": "o014.aljabr2.chapter7.coalgebra-to-hopf-a",
      "sequence": 92,
      "title": "Dari Koaljabar ke Aljabar Hopf"
    },
    {
      "id": "o014.aljabr2.chapter7.coalgebra-to-hopf-b",
      "sequence": 93,
      "title": "Coalgebra To Hopf B"
    },
    {
      "id": "o014.aljabr2.chapter7.beck-monadicity-a",
      "sequence": 94,
      "title": "Teorema Monadisitas Beck"
    },
    {
      "id": "o014.aljabr2.chapter7.beck-monadicity-b",
      "sequence": 95,
      "title": "Beck Monadicity B"
    },
    {
      "id": "o014.aljabr2.chapter7.morita-theory-a",
      "sequence": 96,
      "title": "Teori Morita"
    },
    {
      "id": "o014.aljabr2.chapter7.morita-theory-b",
      "sequence": 97,
      "title": "Morita Theory B"
    },
    {
      "id": "o014.aljabr2.chapter7.morita-theory-c",
      "sequence": 98,
      "title": "Morita Theory C"
    },
    {
      "id": "o014.aljabr2.chapter7.identifying-module-categories",
      "sequence": 99,
      "title": "Mengenali Kategori Modul"
    },
    {
      "id": "o014.aljabr2.chapter7.module-descent",
      "sequence": 100,
      "title": "Penerapan: Penurunan Modul"
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    {
      "id": "o014.aljabr2.chapter7.galois-descent",
      "sequence": 101,
      "title": "Penerapan: Penurunan Galois"
    },
    {
      "id": "o014.aljabr2.chapter7.galois-descent-h1",
      "sequence": 102,
      "title": "Kaitan antara Penurunan Galois dan H1"
    },
    {
      "id": "o014.aljabr2.chapter7.exercises-a",
      "sequence": 103,
      "title": "Latihan"
    },
    {
      "id": "o014.aljabr2.chapter7.exercises-b",
      "sequence": 104,
      "title": "Exercises B"
    },
    {
      "id": "o014.aljabr2.chapter7.exercises-c",
      "sequence": 105,
      "title": "Exercises C"
    },
    {
      "id": "o014.aljabr2.chapter8.simplicial-objects",
      "sequence": 106,
      "title": "Metode Simplisial"
    },
    {
      "id": "o014.aljabr2.chapter8.simplicial-sets",
      "sequence": 107,
      "title": "Himpunan Simplisial"
    },
    {
      "id": "o014.aljabr2.chapter8.nerves-of-categories",
      "sequence": 108,
      "title": "Contoh: Saraf Kategori"
    },
    {
      "id": "o014.aljabr2.chapter8.geometric-realization",
      "sequence": 109,
      "title": "Funktor Realisasi Geometris"
    },
    {
      "id": "o014.aljabr2.chapter8.dold-kan-a",
      "sequence": 110,
      "title": "Korespondensi Dold–Kan"
    },
    {
      "id": "o014.aljabr2.chapter8.dold-kan-b",
      "sequence": 111,
      "title": "Dold Kan B"
    },
    {
      "id": "o014.aljabr2.chapter8.homology-computation",
      "sequence": 112,
      "title": "Perhitungan Homologi"
    },
    {
      "id": "o014.aljabr2.chapter8.bar-construction-a",
      "sequence": 113,
      "title": "Konstruksi bar"
    },
    {
      "id": "o014.aljabr2.chapter8.bar-construction-b",
      "sequence": 114,
      "title": "Bar Construction B"
    },
    {
      "id": "o014.aljabr2.chapter8.bisimplicial-a",
      "sequence": 115,
      "title": "Objek bisimplisial"
    },
    {
      "id": "o014.aljabr2.chapter8.bisimplicial-b",
      "sequence": 116,
      "title": "Bisimplicial B"
    },
    {
      "id": "o014.aljabr2.chapter8.closed-structure",
      "sequence": 117,
      "title": "Struktur Tertutup"
    },
    {
      "id": "o014.aljabr2.chapter8.mapping-cone-revisited",
      "sequence": 118,
      "title": "Meninjau kembali kerucut pemetaan"
    },
    {
      "id": "o014.aljabr2.chapter8.exercises-a",
      "sequence": 119,
      "title": "Latihan"
    },
    {
      "id": "o014.aljabr2.chapter8.exercises-b",
      "sequence": 120,
      "title": "Exercises B"
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    {
      "id": "o014.aljabr2.chapter9.duality-a",
      "sequence": 121,
      "title": "Dualitas"
    },
    {
      "id": "o014.aljabr2.chapter9.duality-rigidity-b",
      "sequence": 122,
      "title": "Dualitas dan Kekakuan (lanjutan)"
    },
    {
      "id": "o014.aljabr2.chapter9.trace-and-dimension",
      "sequence": 123,
      "title": "Dualitas: Jejak dan Dimensi"
    },
    {
      "id": "o014.aljabr2.chapter9.duality-examples-a",
      "sequence": 124,
      "title": "Contoh-contoh dualitas"
    },
    {
      "id": "o014.aljabr2.chapter9.duality-examples-b",
      "sequence": 125,
      "title": "Duality Examples B"
    },
    {
      "id": "o014.aljabr2.chapter9.coendomorphism-coalgebra-a",
      "sequence": 126,
      "title": "Koaljabar endomorfisme"
    },
    {
      "id": "o014.aljabr2.chapter9.coendomorphism-coalgebra-b",
      "sequence": 127,
      "title": "Koaljabar Koendomorfisme (lanjutan)"
    },
    {
      "id": "o014.aljabr2.chapter9.reconstruction-a",
      "sequence": 128,
      "title": "Teorema rekonstruksi"
    },
    {
      "id": "o014.aljabr2.chapter9.reconstruction-b",
      "sequence": 129,
      "title": "Reconstruction B"
    },
    {
      "id": "o014.aljabr2.chapter9.hopf-reconstruction",
      "sequence": 130,
      "title": "Rekonstruksi Aljabar Hopf"
    },
    {
      "id": "o014.aljabr2.chapter9.tannakian-a",
      "sequence": 131,
      "title": "Kategori Tannakian"
    },
    {
      "id": "o014.aljabr2.chapter9.fiber-functor-isomorphisms",
      "sequence": 132,
      "title": "Fiber Functor Isomorphisms"
    },
    {
      "id": "o014.aljabr2.chapter9.tannaka-krein-finite-groups",
      "sequence": 133,
      "title": "Teorema Tannaka--Krein untuk Grup Hingga"
    },
    {
      "id": "o014.aljabr2.chapter9.exercises",
      "sequence": 134,
      "title": "Latihan"
    },
    {
      "id": "o014.aljabr2.appendix1.yoneda-density",
      "sequence": 135,
      "title": "Materi lanjutan tentang kategori abelian"
    },
    {
      "id": "o014.aljabr2.appendix1.compact-presentable-categories",
      "sequence": 136,
      "title": "Objek Kompak dan Kategori Presentabel"
    },
    {
      "id": "o014.aljabr2.appendix1.gabriel-popescu",
      "sequence": 137,
      "title": "Teorema Gabriel--Popescu"
    },
    {
      "id": "o014.aljabr2.appendix1.locally-finite-abelian-categories",
      "sequence": 138,
      "title": "Kategori Abelian yang Hingga Secara Lokal"
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      "id": "o014.aljabr2.appendix-a.exercises",
      "sequence": 139,
      "title": "Latihan Lampiran A"
    },
    {
      "id": "o014.aljabr2.appendix-b.profinite-groups",
      "sequence": 140,
      "title": "Pengantar Objek-Ind dan Objek-Pro"
    },
    {
      "id": "o014.aljabr2.appendix-b.ind-pro-objects",
      "sequence": 141,
      "title": "Tentang Objek-Ind dan Objek-Pro"
    },
    {
      "id": "o014.aljabr2.appendix-b.indization-categories",
      "sequence": 142,
      "title": "Ind-isasi Kategori"
    },
    {
      "id": "o014.aljabr2.appendix-b.indization-functors",
      "sequence": 143,
      "title": "Ind-isasi dan Perluasan Funktor"
    },
    {
      "id": "o014.aljabr2.appendix-b.ind-abelian",
      "sequence": 144,
      "title": "Ind-isasi Kategori Abelian"
    },
    {
      "id": "o014.aljabr2.appendix-b.freyd-mitchell",
      "sequence": 145,
      "title": "Teorema Pembenaman Freyd--Mitchell"
    },
    {
      "id": "o014.aljabr2.appendix-b.exercises",
      "sequence": 146,
      "title": "Latihan Lampiran B"
    }
  ]
}