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Categories and Representation Theory - With A Focus on 2-Categorical Covering Theory (Paperback)
Loot Price: R3,193
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Categories and Representation Theory - With A Focus on 2-Categorical Covering Theory (Paperback)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 17 working days
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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.
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