This book gives a self-contained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2-categorical techniques, including 2-categorical 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 2-categorical generalization of Cohen-Montgomery duality in pseudo-actions 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 2-categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.
Notes
"Ken To Hyogenron by Hideto Asashiba ; Original Japanese language edition published by Saiensu-sha Co., Ltd."
Bibliographic references
Includes bibliographical references (pages 233-235) and index.
Source of description
Description based on publisher supplied metadata and other sources.
Contents
Categories
Representations
Classical covering theory
Basics of 2-categories
2-Categorical covering theory under pseudo-actions of a group
Computations of orbit categories and smash products
Relationships between module categories
2-Categorical covering theory under Colax actions of a category.
ISBN
9781470471507 ((electronic bk.))
OCLC
1350615851
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