基本信息

書名:POD-同調代數方法(第二版)

定價：168.00元

售價：100.8元,便宜67.2元,摺扣60

作者:(德)蓋爾範德(Gelfand S.I.)

齣版社：科學齣版社

齣版日期：2009-01-01

ISBN：9787030234810

字數：

頁碼：

版次：1

裝幀：精裝

開本：16開

商品重量：0.740kg

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內容提要

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 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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