Pendahuluan - Apakah Aljabar Linear Itu?
o014.aljabr2.prelude.linear-algebra
D80 · O014 · id-ID
Teori Kategori dan Metode Homologis
Navigasi 146 unit sumber terjemahan dan dua jembatan penguasaan mandiri. Semua pranala membaca memakai GitHub Pages terkoreksi pada head b6ea8ca709af090f01dca5cba69d4e3b6e603412, bukan pembaca lama di GitHub main.
148 rute unit16 latihan mastery16 solusi mastery864 halaman PDF
Buka tampilan pengajar · Edisi koreksi Zenodo · Repositori publik
Sejarah Singkat Homologi
o014.aljabr2.prelude.homology-history
Tujuan Buku Ini
o014.aljabr2.prelude.book-purpose
Panduan Penggunaan
o014.aljabr2.prelude.reader-guide
Ikhtisar Struktur
o014.aljabr2.prelude.structure-overview
Ucapan Terima Kasih
o014.aljabr2.prelude.acknowledgments
Konvensi
o014.aljabr2.prelude.conventions
Pelengkap Teori Kategori
o014.aljabr2.chapter1.overview
Subkuosien
o014.aljabr2.chapter1.subquotients
Citra, Kocitra, dan Morfisme Ketat
o014.aljabr2.chapter1.images-coimages-strict
Kategori Aditif: Kernel dan Kokernel
o014.aljabr2.chapter1.additive-categories-kernels-cokernels
Perumuman: Kategori Linear atas Gelanggang Komutatif
o014.aljabr2.chapter1.linear-categories-over-commutative-rings
Meninjau Limit melalui Funktor
o014.aljabr2.chapter1.limits-through-functors
Limit Induktif Terfilter
o014.aljabr2.chapter1.filtered-inductive-limits
Ekstensi Kan
o014.aljabr2.chapter1.kan-extensions
Konstruksi Ekstensi Kan melalui Limit
o014.aljabr2.chapter1.kan-extensions-as-limits
Lokalisasi Gabriel--Zisman
o014.aljabr2.chapter1.gabriel-zisman-localization
Ekstensi Kan sepanjang Lokalisasi
o014.aljabr2.chapter1.kan-extensions-along-localization
Teorema Funktor Adjoin
o014.aljabr2.chapter1.adjoint-functor-theorem
Kategori Abelian
o014.aljabr2.chapter2.overview
Definisi Kategori Abelian
o014.aljabr2.chapter2.abelian-category-definition
Mengenal Kompleks
o014.aljabr2.chapter2.first-look-at-complexes
Beberapa Lema Diagram
o014.aljabr2.chapter2.diagram-lemmas
Sekilas tentang Teori Kisi
o014.aljabr2.chapter2.glimpse-of-lattice-theory
Dekomposisi Jumlah Langsung
o014.aljabr2.chapter2.direct-sum-decomposition
Subobjek dan Teorema Isomorfisme
o014.aljabr2.chapter2.subobjects-and-isomorphism-theorems
Objek Sederhana dan Semisederhana
o014.aljabr2.chapter2.simplicity-and-semisimplicity
Funktor Eksak, Objek Injektif, dan Projektif
o014.aljabr2.chapter2.exact-functors-injective-projective-objects
Subkategori Serre dan Grup K0
o014.aljabr2.chapter2.serre-subcategories-and-k0-groups
Kategori Grothendieck
o014.aljabr2.chapter2.grothendieck-categories
Kompleks
o014.aljabr2.chapter3.overview
Kompleks pada Kategori Aditif
o014.aljabr2.chapter3.complexes-over-additive-categories
Kompleks Hom dan Homotopi
o014.aljabr2.chapter3.hom-complex-and-homotopy
Kerucut pemetaan
o014.aljabr2.chapter3.mapping-cone
Kompleks pada kategori lawan
o014.aljabr2.chapter3.opposite-category-complexes
Bikompleks
o014.aljabr2.chapter3.double-complexes
Kompleks pada kategori abelian
o014.aljabr2.chapter3.abelian-category-complexes
Kerucut pemetaan: barisan eksak panjang
o014.aljabr2.chapter3.mapping-cone-and-long-exact-sequences
Latihan: Homologi dan Kohomologi Hochschild
o014.aljabr2.chapter3.exercises-hochschild-homology-and-cohomology
Funktor pemenggalan
o014.aljabr2.chapter3.truncation-functors
Kohomologi bikompleks
o014.aljabr2.chapter3.double-complex-cohomology
Resolusi
o014.aljabr2.chapter3.resolutions
Funktor turunan klasik
o014.aljabr2.chapter3.classical-derived-functors
Contoh: lim^1
o014.aljabr2.chapter3.example-lim1
Contoh: Ext dan Tor
o014.aljabr2.chapter3.ext-tor
Kompleks K-injektif dan K-projektif
o014.aljabr2.chapter3.k-injectives
Latihan
o014.aljabr2.chapter3.exercises
Kategori Bertriangulasi dan Kategori Turunan
o014.aljabr2.chapter4.overview
Definisi Kategori Bertriangulasi
o014.aljabr2.chapter4.triangulated-category-definition
Funktor Kohomologis dan Barisan Eksak Panjang
o014.aljabr2.chapter4.cohomological-functors
Sifat-Sifat Dasar Kategori Bertriangulasi
o014.aljabr2.chapter4.triangulated-basics
Lokalisasi Kategori Bertriangulasi
o014.aljabr2.chapter4.triangulated-localization
Verdier Localization
o014.aljabr2.chapter4.verdier-localization
Kategori Turunan
o014.aljabr2.chapter4.derived-categories
Morfisme dan Ekstensi
o014.aljabr2.chapter4.morphisms-extensions
Funktor Bertriangulasi dan Lokalisasi
o014.aljabr2.chapter4.triangulated-functor-localization
Teori Umum Funktor Turunan
o014.aljabr2.chapter4.derived-functors-general
Funktor Turunan Terbatas
o014.aljabr2.chapter4.bounded-derived-functors
Contoh: RHom
o014.aljabr2.chapter4.rhom
Contoh: RRlim sebagai Limit Homotopi
o014.aljabr2.chapter4.rlim-homotopy-limit
Funktor Turunan Tak Terbatas
o014.aljabr2.chapter4.unbounded-derived-functors
Contoh: Kompleks K-Datar dan otimesL
o014.aljabr2.chapter4.k-flat-derived-tensor-a
Latihan
o014.aljabr2.chapter4.k-flat-derived-tensor-b
Barisan Spektral
o014.aljabr2.chapter5.intro-filtration-grading
Definisi umum barisan spektral
o014.aljabr2.chapter5.general-spectral-sequences
Pasangan eksak
o014.aljabr2.chapter5.exact-couples
Barisan spektral objek diferensial terfiltrasi
o014.aljabr2.chapter5.filtered-differential-spectral-sequence
Barisan spektral kompleks terfiltrasi
o014.aljabr2.chapter5.filtered-complex-spectral-sequence
Barisan spektral bikompleks dan penerapannya
o014.aljabr2.chapter5.bicomplex-spectral-sequences-applications
Sekilas tentang struktur perkalian
o014.aljabr2.chapter5.multiplicative-structures
Latihan
o014.aljabr2.chapter5.exercises
Homologi dan Kohomologi Grup
o014.aljabr2.chapter6.overview-g-modules-resolutions
Homologi dan Kohomologi Grup
o014.aljabr2.chapter6.group-homology-cohomology
Kohomologi berderajat rendah: homomorfisme silang dan ekstensi grup
o014.aljabr2.chapter6.low-degree-cohomology
Modul terinduksi
o014.aljabr2.chapter6.induced-modules
Perubahan grup
o014.aljabr2.chapter6.change-of-group
Meninjau kembali ekstensi grup
o014.aljabr2.chapter6.group-extensions-revisited
Contoh: grup siklik dan grup bebas
o014.aljabr2.chapter6.cyclic-and-free-groups
Subgrup Berindeks Hingga
o014.aljabr2.chapter6.finite-index-subgroups
Barisan spektral Lyndon–Hochschild–Serre
o014.aljabr2.chapter6.lhs-spectral-sequence-a
Lhs Spectral Sequence B
o014.aljabr2.chapter6.lhs-spectral-sequence-b
Operasi Hasil Kali Cawan
o014.aljabr2.chapter6.cup-product
Kohomologi Tate
o014.aljabr2.chapter6.tate-cohomology
Kohomologi grup profinit
o014.aljabr2.chapter6.profinite-cohomology-a
Profinite Cohomology B
o014.aljabr2.chapter6.profinite-cohomology-b
Kohomologi Nonabelian
o014.aljabr2.chapter6.nonabelian-cohomology
Latihan
o014.aljabr2.chapter6.exercises
Teori Monad
o014.aljabr2.chapter7.monoidal-algebras
Contoh: Struktur Diferensial Bergradasi
o014.aljabr2.chapter7.differential-graded-structures
Kategori Monoidal Tertutup
o014.aljabr2.chapter7.closed-monoidal-categories
Studi Kasus: Struktur Tertutup pada Kategori-dg
o014.aljabr2.chapter7.closed-structure-dgcat
Dari Koaljabar ke Aljabar Hopf
o014.aljabr2.chapter7.coalgebra-to-hopf-a
Coalgebra To Hopf B
o014.aljabr2.chapter7.coalgebra-to-hopf-b
Teorema Monadisitas Beck
o014.aljabr2.chapter7.beck-monadicity-a
Beck Monadicity B
o014.aljabr2.chapter7.beck-monadicity-b
Teori Morita
o014.aljabr2.chapter7.morita-theory-a
Morita Theory B
o014.aljabr2.chapter7.morita-theory-b
Morita Theory C
o014.aljabr2.chapter7.morita-theory-c
Mengenali Kategori Modul
o014.aljabr2.chapter7.identifying-module-categories
Penerapan: Penurunan Modul
o014.aljabr2.chapter7.module-descent
Penerapan: Penurunan Galois
o014.aljabr2.chapter7.galois-descent
Kaitan antara Penurunan Galois dan H1
o014.aljabr2.chapter7.galois-descent-h1
Latihan
o014.aljabr2.chapter7.exercises-a
Exercises B
o014.aljabr2.chapter7.exercises-b
Exercises C
o014.aljabr2.chapter7.exercises-c
Metode Simplisial
o014.aljabr2.chapter8.simplicial-objects
Himpunan Simplisial
o014.aljabr2.chapter8.simplicial-sets
Contoh: Saraf Kategori
o014.aljabr2.chapter8.nerves-of-categories
Funktor Realisasi Geometris
o014.aljabr2.chapter8.geometric-realization
Korespondensi Dold–Kan
o014.aljabr2.chapter8.dold-kan-a
Dold Kan B
o014.aljabr2.chapter8.dold-kan-b
Perhitungan Homologi
o014.aljabr2.chapter8.homology-computation
Konstruksi bar
o014.aljabr2.chapter8.bar-construction-a
Bar Construction B
o014.aljabr2.chapter8.bar-construction-b
Objek bisimplisial
o014.aljabr2.chapter8.bisimplicial-a
Bisimplicial B
o014.aljabr2.chapter8.bisimplicial-b
Struktur Tertutup
o014.aljabr2.chapter8.closed-structure
Meninjau kembali kerucut pemetaan
o014.aljabr2.chapter8.mapping-cone-revisited
Latihan
o014.aljabr2.chapter8.exercises-a
Exercises B
o014.aljabr2.chapter8.exercises-b
Dualitas
o014.aljabr2.chapter9.duality-a
Dualitas dan Kekakuan (lanjutan)
o014.aljabr2.chapter9.duality-rigidity-b
Dualitas: Jejak dan Dimensi
o014.aljabr2.chapter9.trace-and-dimension
Contoh-contoh dualitas
o014.aljabr2.chapter9.duality-examples-a
Duality Examples B
o014.aljabr2.chapter9.duality-examples-b
Koaljabar endomorfisme
o014.aljabr2.chapter9.coendomorphism-coalgebra-a
Koaljabar Koendomorfisme (lanjutan)
o014.aljabr2.chapter9.coendomorphism-coalgebra-b
Teorema rekonstruksi
o014.aljabr2.chapter9.reconstruction-a
Reconstruction B
o014.aljabr2.chapter9.reconstruction-b
Rekonstruksi Aljabar Hopf
o014.aljabr2.chapter9.hopf-reconstruction
Kategori Tannakian
o014.aljabr2.chapter9.tannakian-a
Fiber Functor Isomorphisms
o014.aljabr2.chapter9.fiber-functor-isomorphisms
Teorema Tannaka--Krein untuk Grup Hingga
o014.aljabr2.chapter9.tannaka-krein-finite-groups
Latihan
o014.aljabr2.chapter9.exercises
Materi lanjutan tentang kategori abelian
o014.aljabr2.appendix1.yoneda-density
Objek Kompak dan Kategori Presentabel
o014.aljabr2.appendix1.compact-presentable-categories
Teorema Gabriel--Popescu
o014.aljabr2.appendix1.gabriel-popescu
Kategori Abelian yang Hingga Secara Lokal
o014.aljabr2.appendix1.locally-finite-abelian-categories
Latihan Lampiran A
o014.aljabr2.appendix-a.exercises
Pengantar Objek-Ind dan Objek-Pro
o014.aljabr2.appendix-b.profinite-groups
Tentang Objek-Ind dan Objek-Pro
o014.aljabr2.appendix-b.ind-pro-objects
Ind-isasi Kategori
o014.aljabr2.appendix-b.indization-categories
Ind-isasi dan Perluasan Funktor
o014.aljabr2.appendix-b.indization-functors
Ind-isasi Kategori Abelian
o014.aljabr2.appendix-b.ind-abelian
Teorema Pembenaman Freyd--Mitchell
o014.aljabr2.appendix-b.freyd-mitchell
Latihan Lampiran B
o014.aljabr2.appendix-b.exercises
Jembatan Penguasaan 001: Pengejaran Diagram
o014.mastery.diagram-chasing.001
Jembatan Penguasaan 002: Funktor Turunan dan Barisan Spektral
o014.mastery.derived-spectral.002
Latihan dan solusi jembatan mandiri
Fragmen ini materi tambahan independen; karya sumber memiliki 194 latihan dan 117 petunjuk, tetapi tidak menyediakan jawaban atau solusi.
- Latihan 1: o014.mastery.diagram-chasing.001.ex01
- Solusi 1: o014.mastery.diagram-chasing.001.sol01
- Latihan 2: o014.mastery.diagram-chasing.001.ex02
- Solusi 2: o014.mastery.diagram-chasing.001.sol02
- Latihan 3: o014.mastery.diagram-chasing.001.ex03
- Solusi 3: o014.mastery.diagram-chasing.001.sol03
- Latihan 4: o014.mastery.diagram-chasing.001.ex04
- Solusi 4: o014.mastery.diagram-chasing.001.sol04
- Latihan 5: o014.mastery.diagram-chasing.001.ex05
- Solusi 5: o014.mastery.diagram-chasing.001.sol05
- Latihan 6: o014.mastery.diagram-chasing.001.ex06
- Solusi 6: o014.mastery.diagram-chasing.001.sol06
- Latihan 7: o014.mastery.diagram-chasing.001.ex07
- Solusi 7: o014.mastery.diagram-chasing.001.sol07
- Latihan 8: o014.mastery.diagram-chasing.001.ex08
- Solusi 8: o014.mastery.diagram-chasing.001.sol08
- Latihan 1: o014.mastery.derived-spectral.002.ex01
- Solusi 1: o014.mastery.derived-spectral.002.sol01
- Latihan 2: o014.mastery.derived-spectral.002.ex02
- Solusi 2: o014.mastery.derived-spectral.002.sol02
- Latihan 3: o014.mastery.derived-spectral.002.ex03
- Solusi 3: o014.mastery.derived-spectral.002.sol03
- Latihan 4: o014.mastery.derived-spectral.002.ex04
- Solusi 4: o014.mastery.derived-spectral.002.sol04
- Latihan 5: o014.mastery.derived-spectral.002.ex05
- Solusi 5: o014.mastery.derived-spectral.002.sol05
- Latihan 6: o014.mastery.derived-spectral.002.ex06
- Solusi 6: o014.mastery.derived-spectral.002.sol06
- Latihan 7: o014.mastery.derived-spectral.002.ex07
- Solusi 7: o014.mastery.derived-spectral.002.sol07
- Latihan 8: o014.mastery.derived-spectral.002.ex08
- Solusi 8: o014.mastery.derived-spectral.002.sol08
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