最 低 价：￥893.70
定 价：￥993.00
作 者：Sergei I. Gelfand，Yuri I. Manin 著 著
出 版 社：湖南文艺出版社
出版时间：2003-1-1
I S B N：9783540435839
| I. Simplicial Sets 1.1 Triangulated Spaces 1.2 Simplicial Sets 1.3 Simplicial Topological Spaces and the Eilenberg-Zilber Theorem 1.4 Homology and Cohomology 1.5 Sheaves 1.6 The Exact Sequence 1.7 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 |
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