《同調代數方法》是2009年1月1日由科學出版社、科學出版社有限責任公司出版的圖書，作者是蓋爾范德、周伯壎。本書主要選取了國外的一些關於同調代數方法的數學理論知識。
基本介紹
- 書名：同調代數方法
- 頁數： 372頁
- 出版社：科學出版社
- 出版時間：2009年1月1日
圖書信息,內容簡介,作者簡介,目錄,
圖書信息
外文書名: methods of homological algebra (second edition)
叢書名: 國外數學名著系列（續一）（影印版）37
精裝: 372頁
正文語種: 英語
開本: 16
isbn: 9787030234810
條形碼: 9787030234810
商品尺寸: 24.2 x 17.2 x 2.4 cm
商品重量: 739 g
內容簡介
《國外數學名著系列(續1)(影印版)37:同調代數方法(第2版)》主要內容：Homologicalalgebrafirstaroseasalanguagefordescribingtopologicalprospectsofgeometricalobjects.Aswitheverysuccessfullanguageitquicklyexpandeditscoverageandsemantics,anditscontemporaryapplicationsaremanyanddiverse.Thismodernapproachtohomologicalalgebra,bytwoleadingwritersinthefield,isbasedonthesystematicuseofthelanguageandideasofderivedcategoriesandderivedfunctors.Relationswithstandardcohomologytheory(sheafcohomology,spectralsequences,etc.)aredescribed.Inmostcasescompleteproofsaregiven.Basicconceptsandresultsofhomotopicalalgebraarealsopresented.Thebookaddressespeoplewhowanttolearnamodernapproachtohomologicalalgebraandtouseitintheirwork.Forthesecondeditiontheauthorshavemadenumerouscorrections.
作者簡介
作者：(德國)蓋爾范德(SergeiI.Gelfand)
目錄
Ⅰ. Simplicial Sets
Ⅰ.1 Triangulated Spaces
Ⅰ.2 Simplicial Sets
Ⅰ.3 Simplicial Topological Spaces and the Eilenberg-Zilber Theorem
Ⅰ.4 Homology and Cohomology
Ⅰ.5 Sheaves
Ⅰ.6 The Exact Sequence
Ⅰ.7 Complexes
Ⅱ. Main Notions of the Category Theory
Ⅱ.1 The Language of Categories and Functors
Ⅱ.2 Categories and Structures, Equivalence of Categories
Ⅱ.3 Structures and Categories. Representable Functors
Ⅱ.4 Category Approach to the Construction of Geometrical Objects
Ⅱ.5 Additive and Abelian Categories
Ⅱ.6 Functors in Abelian Categories
Ⅲ. Derived Categories and Derived Functors
Ⅲ.1 Complexes as Generalized Objects
Ⅲ.2 Derived Categories and Localization
Ⅲ.3 Triangles as Generalized Exact Triples
Ⅲ.4 Derived Category as the Localization of Homotopic Category
Ⅲ.5 The Structure of the Derived Category
Ⅲ.6 Derived Functors
Ⅲ.7 Derived Functor of the Composition. Spectral Sequence
Ⅲ.8 Sheaf Cohomology
Ⅳ.Triangulated categories
Ⅳ. Triangulated Categories
Ⅳ.1 Triangulated Categories
Ⅳ.2 Derived Categories Are Triangulated
Ⅳ.3 An Example: The Triangulated Category of A-Modules
Ⅳ.4 Cores
Ⅴ. Introduction to Homotopic Algebra
Ⅴ.1 Closed Model Categories
Ⅴ.2 Homotopic Characterization of Weak Equivalences
Ⅴ.3 DG-Algebras as a Closed Model Category
Ⅴ.4 Minimal Algebras
Ⅴ.5 EquⅣalence of Hoinotopy Categories
References
Index
