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同调代数方法(第二版)
  • 书号:9787030234810
    作者:Manin, Yuri I.
  • 外文书名:Methods of Homological Algebra
  • 丛书名:国外数学名著系列(影印版)
  • 装帧:精装
    开本:B5
  • 页数:396
    字数:469000
    语种:英文
  • 出版社:科学出版社
    出版时间:2009-01
  • 所属分类:
  • 定价: ¥168.00元
    售价: ¥168.00元
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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 modem approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.
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目录

  • Ⅰ SimplicialSets
    Ⅰ.1 Triarignlated Spaces
    Ⅰ.2 Simplicial Sets
    Ⅰ.3 Simplicial Topological Spaces and the Eilcribcrg-Zilber Theorem
    Ⅰ.4 Horriology and Cohomology
    Ⅰ.5 Sheaves
    Ⅰ.6 The Exact Sequence
    Ⅰ.7 Cornplcxcs
    Ⅱ. Main Notions of the Category Theory
    Ⅱ.1 Thc Language of Categorics and Functors
    Ⅱ.2 Categories arid Structures,Equivalence of Categories
    Ⅱ.3 Structurcsa nd Categories. Represmtablc Functors
    Ⅱ.4 Category Approach to the Coristrlictiorl of Gcomet.r ical Objects
    Ⅱ.5 Additive and Ahelian Categories
    Ⅱ.6 Functors iri Abelian Categories
    Ⅲ. Derived Categories and Derived Functors
    Ⅲ.1 Complexes as Generalized Objccts
    Ⅲ.2 Derived Categories arid Localization
    Ⅲ.3 Triangles as Generalized Exact Triplcs
    Ⅲ.4 Derived Category as the Localization of Homotopic Category
    Ⅲ.5 Thr Strlictllre of the Derivcd Category
    Ⅲ.6 Derivrd Functors
    Ⅲ.7 Dcrivtd Functor of the Composition. Spectral Sequence
    Ⅲ.8 Sheaf Coliornology
    Ⅳ. Triangulated Categories
    Ⅳ.1 Triangnlatcd Categories
    Ⅳ.2 Derived Categories Are Triangulated
    Ⅳ.3 An Example: The Triangulated Category of Λ-Modules
    Ⅳ.4 Cores
    Ⅴ. Introduction to Homotopic Algebra
    Ⅴ.1 Closed Model Categories
    Ⅴ.2 Homotopic Characterization of Weak Equivalences
    Ⅴ.3 DG-Algcbras as a Closed Model Category
    Ⅴ.4 Mirlirrlal Algebras
    Ⅴ.5 Equivalence of Horrlotopy Categories
    References
    Index
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