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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
Available Formats:
Hardcover ISBN: 978-0-8218-2877-9
Product Code: CRMM/17
179 pp
List Price: $64.00 MAA Member Price:$57.60
AMS Member Price: $51.20 Electronic ISBN: 978-1-4704-3862-3 Product Code: CRMM/17.E 179 pp List Price:$60.00
MAA Member Price: $54.00 AMS Member Price:$48.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $96.00 MAA Member Price:$86.40
AMS Member Price: $76.80 Click above image for expanded view 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 Available Formats:  Hardcover ISBN: 978-0-8218-2877-9 Product Code: CRMM/17 179 pp  List Price:$64.00 MAA Member Price: $57.60 AMS Member Price:$51.20
 Electronic ISBN: 978-1-4704-3862-3 Product Code: CRMM/17.E 179 pp
 List Price: $60.00 MAA Member Price:$54.00 AMS Member Price: $48.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$96.00
MAA Member Price: $86.40 AMS Member Price:$76.80
• Book Details

CRM Monograph Series
Volume: 172002
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.

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
• 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
• Request Review Copy
Volume: 172002
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.

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
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