Categories and representation theory : with a focus on 2-categorical covering theory
著者
書誌事項
Categories and representation theory : with a focus on 2-categorical covering theory
（Mathematical surveys and monographs, v. 271）
American Mathematical Society, c2022
- : pbk
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Ken to hyōgenron
圏と表現論
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注記
Original Japanese language ed. published by Saiensu-sha, c2019
Includes bibliographical references (p. 233-235) and index
内容説明・目次
内容説明
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.
目次
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
Set theory for the foundation of category theorem
Supplement to the original version
Bibliography
Index
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