Woodslane | Book - 9781470464844

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Categories and Representation Theory

With A Focus on 2-Categorical Covering Theory

ISBN-13: 9781470464844
Publisher: AMERICAN MATHEMATICAL SOCIETY
Imprint: AMERICAN MATHEMATICAL SOCIETY
By Hideto Asashiba
Price: AUD $321.00
Stock: 0 in stock
Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
Local release date: 30/03/2023
Format: Paperback (254.00mm X 178.00mm) 250 pages Weight: 462g
Categories: Algebra [PBF]Algebraic geometry [PBMW]

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Table of Contents
Google Preview: 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.; Hideto Asashiba, Shizuoka University, Suruga-ku, Shizuoka, Japan, Kyoto University, Sakyo-ku, Kyoto, Japan, and Osaka Metropolitan University Advanced Mathematical Institute, Sumiyoshi-ku, Osaka, Japan.; 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; Google Preview content

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Categories and Representation Theory

With A Focus on 2-Categorical Covering Theory