Methods of Homological Algebra

1. Front Matter

   Pages I-XVIII

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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 357-373

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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 about a modern approach to homological algebra and to use it in their work.

• Cohomology
• Homological algebra
• Sheaf cohomology
• category theory
• homotopical algebra

• American Mathematical Society, Providence, USA

  Sergei I. Gelfand

• MPI für Mathematik, Bonn, Germany

  Yuri I. Manin

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