Softcover ISBN:  9781470464844 
Product Code:  SURV/271 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470471507 
Product Code:  SURV/271.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470464844 
eBook: ISBN:  9781470471507 
Product Code:  SURV/271.B 
List Price:  $250.00 $187.50 
MAA Member Price:  $225.00 $168.75 
AMS Member Price:  $200.00 $150.00 
Softcover ISBN:  9781470464844 
Product Code:  SURV/271 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470471507 
Product Code:  SURV/271.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470464844 
eBook ISBN:  9781470471507 
Product Code:  SURV/271.B 
List Price:  $250.00 $187.50 
MAA Member Price:  $225.00 $168.75 
AMS Member Price:  $200.00 $150.00 

Book DetailsMathematical Surveys and MonographsVolume: 271; 2022; 240 ppMSC: Primary 18; 16
This book gives a selfcontained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2categorical techniques, including 2categorical covering theory. The book has few prerequisites beyond linear algebra and elementary ring theory, but familiarity with the basics of representations of quivers and of category theory will be helpful. In addition to providing an introduction to category theory, the book develops useful tools such as quivers, adjoints, string diagrams, and tensor products over a small category; gives an exposition of new advances such as a 2categorical generalization of CohenMontgomery duality in pseudoactions of a group; and develops the moderation level of categories, first proposed by Levy, to avoid the set theoretic paradox in category theory.
The book is accessible to advanced undergraduate and graduate students who would like to study the representation theory of algebras, and it contains many exercises. It can be used as the textbook for an introductory course on the category theoretic approach with an emphasis on 2categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.
ReadershipUndergraduate and graduate students interested in the representation theory of algebras and 2categorical covering theory.

Table of Contents

Chapters

Categories

Representations

Classical covering theory

Basics of 2categories

2categorical covering theory under pseudoactions of a group

Computations of orbit categories and smash products

Relationships between module categories

2categorical covering theory under colax actions of a category

Set theory for the foundation of category theorem

Supplement to the original version


Additional Material

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This book gives a selfcontained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2categorical techniques, including 2categorical covering theory. The book has few prerequisites beyond linear algebra and elementary ring theory, but familiarity with the basics of representations of quivers and of category theory will be helpful. In addition to providing an introduction to category theory, the book develops useful tools such as quivers, adjoints, string diagrams, and tensor products over a small category; gives an exposition of new advances such as a 2categorical generalization of CohenMontgomery duality in pseudoactions of a group; and develops the moderation level of categories, first proposed by Levy, to avoid the set theoretic paradox in category theory.
The book is accessible to advanced undergraduate and graduate students who would like to study the representation theory of algebras, and it contains many exercises. It can be used as the textbook for an introductory course on the category theoretic approach with an emphasis on 2categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.
Undergraduate and graduate students interested in the representation theory of algebras and 2categorical covering theory.

Chapters

Categories

Representations

Classical covering theory

Basics of 2categories

2categorical covering theory under pseudoactions of a group

Computations of orbit categories and smash products

Relationships between module categories

2categorical covering theory under colax actions of a category

Set theory for the foundation of category theorem

Supplement to the original version