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Non-Abelian Homological Algebra and Its Applications : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - Hvedri Inassaridze

Non-Abelian Homological Algebra and Its Applications


Hardcover Published: 31st October 1997
ISBN: 9780792347187
Number Of Pages: 266

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While in classical (abelian) homological algebra additive functors from abelian (or additive) categories to abelian categories are investigated , non- abelian homological algebra deals with non-additive functors and their homological properties , in particular with functors having values in non-abelian categories. Such functors haveimportant applications in algebra, algebraic topology, functional analysis, algebraic geometry and other principal areas of mathematics. To study homological properties of non-additive functors it is necessary to define and investigate their derived functors and satellites. It will be the aim of this book based on the results of researchers of A. Razmadze Mathematical Institute of the Georgian Academy of Sciences devoted to non-abelian homological algebra. The most important considered cases will be functors from arbitrary categories to the category of modules, group valued functors and commutative semigroup valued functors. In Chapter I universal sequences of functors are defined and in­ vestigated with respect to (co)presheaves of categories, extending in a natural way the satellites of additive functors to the non-additive case and generalizing the classical relative homological algebra in additive categories to arbitrary categories. Applications are given in the furth­ coming chapters. Chapter II is devoted to the non-abelian derived functors of group valued functors with respect to projective classes using projective pseu­ dosimplicial resolutions. Their functorial properties (exactness, Milnor exact sequence, relationship with cotriple derived functors, satellites and Grothendieck cohomology, spectral sequence of an epimorphism, degree of an arbitrary functor) are established and applications to ho­ mology and cohomology of groups are given.

Universal Sequences of Functors
Derived Functors
Extensions and Cohomology of Monoids with Coefficients in Semimodules
Cohomology of Algebraic Theories and MacLane (co)Homology of Rings
Non-Abelian Homology and Cohomology of Groups
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792347187
ISBN-10: 0792347188
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 266
Published: 31st October 1997
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 2.54
Weight (kg): 0.59

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