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  3. From Categories to Homotopy Theory
  • Cited by 15
Publisher:
Cambridge University Press
Online publication date:
April 2020
Print publication year:
2020
Online ISBN:
9781108855891
DOI:
https://doi.org/10.1017/9781108855891
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
Cambridge Studies in Advanced Mathematics (188)
Information

Book description

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.

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 Source: 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 Source: MathSciNet (https://mathscinet.ams.org)

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Contents

Contents
  • 1 - Basic Notions in Category Theory
    pp 7-26
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