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Methods of Homological Algebra

  • Book
  • © 2003

Overview

Authors:
  1. Sergei I. Gelfand

    1. American Mathematical Society, Providence, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Yuri I. Manin

    1. Max Planck Institute for Mathematics, Bonn, Germany

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XX
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  2. Simplicial Sets

    • Sergei I. Gelfand, Yuri I. Manin
    Pages 1-55

  3. Main Notions of the Category Theory

    • Sergei I. Gelfand, Yuri I. Manin
    Pages 57-138

  4. Derived Categories and Derived Functors

    • Sergei I. Gelfand, Yuri I. Manin
    Pages 139-238

  5. Triangulated Categories

    • Sergei I. Gelfand, Yuri I. Manin
    Pages 239-290

  6. Introduction to Homotopic Algebra

    • Sergei I. Gelfand, Yuri I. Manin
    Pages 291-356

  7. Back Matter

    Pages 357-374
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Keywords

About this book

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 modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

Reviews

From the reviews of the second edition:

"This is the revised edition of a modern approach to homological algebra by two leading writers in the field. It is based on the systematic use of the language and technics of derived categories and derived functors. The reader has all the basic material and a lot of examples … . This book can be used by students just beginning to study homological algebra, as well as by specialists who will find there some points which have never been clarified in the literature." (Jean-Claude Thomas, Belgian Mathematical Society – Simon Stevin Bulletin, Vol. 10 (2), 2003)

"It is a pleasure to have on the desk this second edition from a new classical text in mathematics. … this text has to be seen as part of the general process of unification in mathematics." (Bernd Richter, Zentralblatt MATH, Vol. 1006, 2003)

Authors and Affiliations

  • American Mathematical Society, Providence, USA

    Sergei I. Gelfand

  • Max Planck Institute for Mathematics, Bonn, Germany

    Yuri I. Manin

Bibliographic Information

  • Book Title: Methods of Homological Algebra

  • Authors: Sergei I. Gelfand, Yuri I. Manin

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-12492-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Hardcover ISBN: 978-3-540-43583-9Published: 26 November 2002

  • Softcover ISBN: 978-3-642-07813-2Published: 06 December 2010

  • eBook ISBN: 978-3-662-12492-5Published: 09 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 2

  • Number of Pages: XX, 372

  • Additional Information: Originally published as a monograph

  • Topics: Category Theory, Homological Algebra

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