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categories and homological algebra schapira [pdf]

Categories and Homological Algebra by Pierre Schapira

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About this book :-
Categories and Homological Algebra written by Pierre Schapira.
These notes are introduce the reader to the language of categories and to present the basic notions of homological algebra, first from an elementary point of view, with the notion of derived functors, next with a more sophisticated approach, with the introduction of triangulated and derived categories.
After having introduced the basic concepts of category theory and in particular those of projective and inductive limits, this text treat with some details additive and abelian categories and construct the derived functors. It also introduce the reader to the concepts of triangulated and derived categories. Our exposition of these topics is rather sketchy, and the reader is encouraged to consult the literature.

Book Detail :-
Title: Categories and Homological Algebra
Author(s): Pierre Schapira
Year: 2011
Pages: 125
Type: PDF
Language: English
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Book Contents :-
Categories and Homological Algebra written by Pierre Schapira cover the following topics.
The language of categories
Sets and maps, Modules and linear maps, Categories and functors, The Yoneda Lemma, Representable functors, adjoint functors, Exercises
Products and coproducts, Kernels and cokernels, Limits, Properties of limits, Filtrant inductive limits, Exercises
Additive categories
Additive categories, Complexes in additive categories, Double complexes, Simplicial constructions, Exercises
Abelian categories
Abelian categories, Exact functors, Injective and projective objects, Complexes in abelian categories, Resolutions, Derived functors, Koszul complexes, Exercises
Localization of categories, Localization of subcategories, Localization of functors, Exercises
Triangulated categories
Triangulated categories, The homotopy category K(C), Localization of triangulated categories, Exercises
Derived categories
Derived categories, Resolutions, Derived functors, Bifunctors, Exercises


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