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Acyclic Models
 
Michael Barr Peter Redpath Emeritus Professor of Pure Mathematics, McGill University, Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Acyclic Models
Hardcover ISBN:  978-0-8218-2877-9
Product Code:  CRMM/17
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-1-4704-3862-3
Product Code:  CRMM/17.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-2877-9
eBook: ISBN:  978-1-4704-3862-3
Product Code:  CRMM/17.B
List Price: $225.00 $170.00
MAA Member Price: $202.50 $153.00
AMS Member Price: $180.00 $136.00
Acyclic Models
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Acyclic Models
Michael Barr Peter Redpath Emeritus Professor of Pure Mathematics, McGill University, Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Hardcover ISBN:  978-0-8218-2877-9
Product Code:  CRMM/17
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-1-4704-3862-3
Product Code:  CRMM/17.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-2877-9
eBook ISBN:  978-1-4704-3862-3
Product Code:  CRMM/17.B
List Price: $225.00 $170.00
MAA Member Price: $202.50 $153.00
AMS Member Price: $180.00 $136.00
  • Book Details
     
     
    CRM Monograph Series
    Volume: 172002; 179 pp
    MSC: 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.

    Titles in this series are co-published with the Centre de recherches mathématiques.

    Readership

    Graduate 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
    • Cartan-Eilenberg 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 self-contained 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 172002; 179 pp
MSC: 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.

Titles in this series are co-published with the Centre de recherches mathématiques.

Readership

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
  • Cartan-Eilenberg 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 self-contained 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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