From Categories to Homotopy Theory : Cambridge Studies in Advanced Mathematics - Birgit Richter

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From Categories to Homotopy Theory

By: Birgit Richter

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Hardcover | 16 April 2020

At a Glance

Hardcover
402 Pages

Dimensions(cm)
22.86 x 15.24 x 2.69

Hardcover

RRP $119.95

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Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.

Industry Reviews

'It would be an excellent text for a graduate student just finishing introductory coursework and wanting to know about techniques in modern homotopy theory.' Julie Bergner
'... this book attempts to bridge the gap between the basic theory and the application of categorical methods to homotopy theory, which has been the subject of some recent exciting developments ... the book would be very useful for beginner graduate students in homotopy theory.' Hollis Williams, IMA website
'The book has been thoughtfully written with students in mind, and contains plenty of pointers to the literature for those who want to pursue a subject further. Readers will find themselves taken on an engaging journey by a true expert in the field, who brings to the material both insight and style.' Daniel Dugger, MathSciNet (https://mathscinet.ams.org)

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