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.
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.
Categorisation is an essential and unavoidable instrumentality for conceptually navigating a world - indeed for being able to conceptualise a world to be navigated.Classification is a pivotal...
This book contains the definitive statement of Franz Brentano's views on meta physics. It is made up of essays which were dictated by Brentano during the last ten years of his life, between 1907 and...
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