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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
** Edition: **
** Author(s): ** Pierre Schapira
** Publisher: **
** Series: **
** Year: ** 2011
** Pages: ** 125
** Type: ** PDF
** Language: ** English
** ISBN: **
** Country: **
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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
**Limits**

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**

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

**Note:-**

We are not the owner of this book/notes. We provide it which is already avialable on the internet. For any further querries please contact us. We never SUPPORT PIRACY. This copy was provided for students who are financially troubled but want studeing to learn. If You Think This Materials Is Useful, Please get it legally from the PUBLISHERS. Thank you.

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