Homological Algebra of Semimodules and Semicontramodules: Semi-infinite Homological Algebra of Associative Algebraic Structures

EBook Description: his is a monograph in semi-infinite homological algebra, concentrated mostly on the semi-infinite theory of associative algebraic structures, but including also some material on the semi-infinite homology and cohomology of Lie algebras and topological groups. The main objects of study are the double-sided derived functors SemiExt and SemiTor, and the phenomenon of comodule-contramodule correspondence, connecting them with the more conventional, one-sided Ext and CtrTor. Contramodules, introduced originally by Eilenberg and Moore in 1960's but almost forgotten for four decades, play a very prominent role in this book, with many versions of them introduced and discussed. Among other topics considered in the monograph there are the semi-infinite model category structures and the relative nohomogeneous Koszul duality.

Homological Algebra

Introduction to Homological Algebra

Introduction to Homological Algebra

Projective Geometry and Homological Algebra

Projective Geometry and Homological Algebra

Gorenstein Rings and Modules

Gorenstein Rings and Modules

Abstract and Concrete Categories The Joy of Cats

Abstract and Concrete Categories The Joy of Cats

Toposes, Triples and Theories

Toposes, Triples and Theories

Introduction to Homological Algebra pdf

Introduction to Homological Algebra pdf

A Gentle Introduction to Category Theory The Calculational Approach

A Gentle Introduction to Category Theory The Calculational Approach

Abelian Categories

Abelian Categories

A Course in Homological Algebra

This classic book provides a broad introduction to homological algebra, including a comprehensive set of exercises. Since publication of the first edition homological algebra has found a large number of applications in many different fields. Today, it is a truly indispensable tool in fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In this new edition, the authors have selected a number of different topics and describe some of the main applications and results to illustrate the range and depths of these developments. The background assumes little more than knowledge of the algebraic theories groups and of vector spaces over a field.

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