POD-同调代数方法(第二版) (德)盖尔范德(Gelfand S.I.) 科学出版社 下载 mobi epub pdf 电子书 2024

基本信息

书名:POD-同调代数方法(第二版)

定价：168.00元

售价：100.8元,便宜67.2元,折扣60

作者:(德)盖尔范德(Gelfand S.I.)

出版社：科学出版社

出版日期：2009-01-01

ISBN：9787030234810

字数：

页码：

版次：1

装帧：精装

开本：16开

商品重量：0.740kg

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内容提要

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 moderapproach to homological algebra， by two leading writers ithe field， is based othe 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. Imost cases plete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to leara moderapproach to homological algebra and to use it itheir work. For the second editiothe authors have made numerous corrections.

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．MaiNotions 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 Constructioof Geometrical Objects
Ⅱ．5 Additive and AbeliaCategories
Ⅱ．6 Functors iAbeliaCategories

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 Localizatioof 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 AExample： The Triangulated Category of A-Modules
Ⅳ．4 Cores

Ⅴ．Introductioto Homotopic Algebra
Ⅴ．1 Closed Model Categories
Ⅴ．2 Homotopic Characterizatioof Weak Equivalences．
Ⅴ．3 DG-Algebras as a Closed Model Category
Ⅴ．4 Minimal Algebras
Ⅴ．5 Equivalence of Homotopy Categories

References
Index

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