同调代数方法（续一影印版第二版）

定　价：¥86.00

作　者：	（德）盖尔范德（Gelfand S.I.）等著
出版社：	科学出版社
丛编项：	国外数学名著系列
标　签：	组合理论

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ISBN：	9787030234810	出版时间：	2009-01-01	包装：	精装
开本：	16开	页数：	372	字数：

内容简介

　　Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics， and its contemporary applications are many and diverse. This modern approach to homological algebra， by two leading writers in the field， is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory （sheaf cohomology， spectral sequences， etc.） are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

作者简介

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图书目录

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 Cohmology
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.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 Homotopy Categories
References
Index