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| 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.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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