同调代数方法

图书标准信息

• 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