同调代数方法
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作者[德]盖尔范德（Gelfand S.I.）、[德]盖尔范德（Gelfand S.I.） 著
出版社科学出版社
出版时间2009-01
版次1
装帧精装
货号34-1
上书时间2024-11-23
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- 作者 [德]盖尔范德（Gelfand S.I.）、[德]盖尔范德（Gelfand S.I.） 著
- 出版社 科学出版社
- 出版时间 2009-01
- 版次 1
- ISBN 9787030234810
- 定价 86.00元
- 装帧 精装
- 开本 16开
- 纸张 胶版纸
- 页数 372页
- 字数 469千字
- 正文语种 英语
- 【内容简介】
- Homologicalalgebrafirstaroseasalanguagefordescribingtopologicalprospectsofgeometricalobjects.Aswitheverysuccessfullanguageitquicklyexpandeditscoverageandsemantics,anditscontemporaryapplicationsaremanyanddiverse.Thismodernapproachtohomologicalalgebra,bytwoleadingwritersinthefield,isbasedonthesystematicuseofthelanguageandideasofderivedcategoriesandderivedfunctors.Relationswithstandardcohomologytheory(sheafcohomology,spectralsequences,etc.)aredescribed.Inmostcasescompleteproofsaregiven.Basicconceptsandresultsofhomotopicalalgebraarealsopresented.Thebookaddressespeoplewhowanttolearnamodernapproachtohomologicalalgebraandtouseitintheirwork.Forthesecondeditiontheauthorshavemadenumerouscorrections.
- 【目录】
-
Ⅰ.SimplicialSets
Ⅰ.1TriangulatedSpaces
Ⅰ.2SimplicialSets
Ⅰ.3SimplicialTopologicalSpacesandtheEilenberg-ZilberTheorem
Ⅰ.4HomologyandCohomology
Ⅰ.5Sheaves
Ⅰ.6TheExactSequence
Ⅰ.7Complexes
Ⅱ.MainNotionsoftheCategoryTheory
Ⅱ.1TheLanguageofCategoriesandFunctors
Ⅱ.2CategoriesandStructures，EquivalenceofCategories
Ⅱ.3StructuresandCategories.RepresentableFunctors
Ⅱ.4CategoryApproachtotheConstructionofGeometricalObjects
Ⅱ.5AdditiveandAbelianCategories
Ⅱ.6FunctorsinAbelianCategories
Ⅲ.DerivedCategoriesandDerivedFunctors
Ⅲ.1ComplexesasGeneralizedObjects
Ⅲ.2DerivedCategoriesandLocalization
Ⅲ.3TrianglesasGeneralizedExactTriples
Ⅲ.4DerivedCategoryastheLocalizationofHomotopicCategory
Ⅲ.5TheStructureoftheDerivedCategory
Ⅲ.6DerivedFunctors
Ⅲ.7DerivedFunctoroftheComposition.SpectralSequence
Ⅲ.8SheafCohomology
Ⅳ.Triangulatedcategories
Ⅳ.TriangulatedCategories
Ⅳ.1TriangulatedCategories
Ⅳ.2DerivedCategoriesAreTriangulated
Ⅳ.3AnExample：TheTriangulatedCategoryofA-Modules
Ⅳ.4Cores
Ⅴ.IntroductiontoHomotopicAlgebra
Ⅴ.1ClosedModelCategories
Ⅴ.2HomotopicCharacterizationofWeakEquivalences
Ⅴ.3DG-AlgebrasasaClosedModelCategory
Ⅴ.4MinimalAlgebras
Ⅴ.5EquⅣalenceofHoinotopyCategories
References
Index
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