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From Categories to Homotopy Theory by Birgit Richter (Universität Hamburg) at Abbey's Bookshop,
From Categories to Homotopy Theory
— —
Birgit Richter (Universität Hamburg)

From Categories to Homotopy Theory

Birgit Richter (Universität Hamburg)

$105.95

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English
Cambridge University Press
16 April 2020
Algebraic topology
Series: Cambridge Studies in 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.
By:  
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Dimensions:   Height: 235mm,  Width: 156mm,  Spine: 26mm
Weight:   680g
ISBN:   9781108479622
ISBN 10:   1108479626
Series:   Cambridge Studies in Advanced Mathematics
Pages:   400
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Introduction; Part I. Category Theory: 1. Basic notions in category theory; 2. Natural transformations and the Yoneda lemma; 3. Colimits and limits; 4. Kan extensions; 5. Comma categories and the Grothendieck construction; 6. Monads and comonads; 7. Abelian categories; 8. Symmetric monoidal categories; 9. Enriched categories; Part II. From Categories to Homotopy Theory: 10. Simplicial objects; 11. The nerve and the classifying space of a small category; 12. A brief introduction to operads; 13. Classifying spaces of symmetric monoidal categories; 14. Approaches to iterated loop spaces via diagram categories; 15. Functor homology; 16. Homology and cohomology of small categories; References; Index.

Birgit Richter is Professor of Mathematics at Universität Hamburg. She is the co-editor of Structured Ring Spectra (2004) and New Topological Contexts for Galois Theory and Algebraic Geometry (2009).

Reviews for From Categories to Homotopy Theory

'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


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