Categories to homotopy theory
Series: Cambridge studies in advanced mathematics ; 188Publication details: Cambridge University Press, 2020. Cambridge:Description: x, 390 p. : hb, 24 cmISBN:- 9781108479622
- 514.24 RIC
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IIT Gandhinagar General Stacks | General | 514.24 RIC (Browse shelf(Opens below)) | 1 | Available | 030194 |
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514.24 BAR Foundations of stable homotopy theory | 514.24 BAU Algebraic homotopy | 514.24 CIS Higher categories and homotopical algebra | 514.24 RIC Categories to homotopy theory | 514.3 JOH Stone spaces | 514.3 WEE Shape of space | 514.322 YAN Elementary point set topology: a transition to advanced mathematics |
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.
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