Hardcover ISBN:  9780821828779 
Product Code:  CRMM/17 
179 pp 
List Price:  $64.00 
MAA Member Price:  $57.60 
AMS Member Price:  $51.20 
Electronic ISBN:  9781470438623 
Product Code:  CRMM/17.E 
179 pp 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 

Book DetailsCRM Monograph SeriesVolume: 17; 2002MSC: Primary 18;
Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background.
It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology.
The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers.ReadershipGraduate students and research mathematicians interested in category theory and homological algebra.

Table of Contents

Chapters

Categories

Abelian categories and homological algebra

Chain complexes and simplicial objects

Triples à la mode de Kan

The main acyclic models theorem

CartanEilenberg Cohomology

Other applications in algebra

Applications in topology


Reviews

I like this book. It covers ground not often explored in textbooks … with a perspective … complementary to the usual.
Zentralblatt MATH 
This much needed book provides a clear and selfcontained account of the cotriple approach to the cohomology theory of algebraic objects. Written by one of the founders of the subject, it will prove useful both as a teaching text and reference text for researchers.
Mathematical Reviews


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 Book Details
 Table of Contents
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Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background.
It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology.
The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers.
Graduate students and research mathematicians interested in category theory and homological algebra.

Chapters

Categories

Abelian categories and homological algebra

Chain complexes and simplicial objects

Triples à la mode de Kan

The main acyclic models theorem

CartanEilenberg Cohomology

Other applications in algebra

Applications in topology

I like this book. It covers ground not often explored in textbooks … with a perspective … complementary to the usual.
Zentralblatt MATH 
This much needed book provides a clear and selfcontained account of the cotriple approach to the cohomology theory of algebraic objects. Written by one of the founders of the subject, it will prove useful both as a teaching text and reference text for researchers.
Mathematical Reviews