基本介紹
- 書名：國外數學名著系列37：同調代數方法
- 作者：(德國)蓋爾范德 (Sergei I.Gelfand)
- 原版名稱：Methods of Homological Algebra (Second Edition)
- ISBN：9787030234810
- 頁數：372頁
- 出版社：科學出版社
- 出版時間：2009年1月1日
- 裝幀：精裝
- 開本：16
- 語言：英語
內容簡介,目錄,
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：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.
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
