Non-Abelian Homological Algebra and Its Applications / Edition 1

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This book exposes methods of non-abelian homological algebra, such as the theory of satellites in abstract categories with respect to presheaves of categories and the theory of non-abelian derived functors of group valued functors. Applications to K-theory, bivariant K-theory and non-abelian homology of groups are given. The cohomology of algebraic theories and monoids are also investigated. The work is based on the recent work of the researchers at the A. Razmadze Mathematical Institute in Tbilisi, Georgia.
Audience: This volume will be of interest to graduate students and researchers whose work involves category theory, homological algebra, algebraic K-theory, associative rings and algebras; algebraic topology, and algebraic geometry.

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Editorial Reviews

Synthesizes findings of research mathematicians at the Georgian Academy of Sciences regarding the branch of algebra that deals with non-additive functors and their homological properties. Emphasizes functors from arbitrary categories to the category of modules, group valued functors, and commutative semigroup valued functors. Defines universal sequences of functors and discusses them in terms of presheaves of categories and extended cases, establishes the functorial properties of the non-abelian derived functors of group valued functors and demonstrates applications to homology and cohomology, treats the cohomology of monoids with coefficients in semimodules, explains the MacLane cohomology and homology of rings, obtains the algebraic and topological K-functors, and introduces a non-abelian tensor product of groups for non-compatible actions. No index. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780792347187
  • Publisher: Springer Netherlands
  • Publication date: 10/31/1997
  • Series: Mathematics and Its Applications (closed) Series, #421
  • Edition description: 1997
  • Edition number: 1
  • Pages: 266
  • Product dimensions: 0.75 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Introduction. 1. Universal Sequences of Functors. 2. Derived Functors. 3. Extensions and Cohomology of Monoids with Coefficients in Semimodules. 4. Cohomology of Algebraic Theories and MacLane (co)Homology of Rings. 5. K-Functors. 6. Non-Abelian Homology and Cohomology of Groups. References.

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