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Categorical Homotopy Theory by Emily Riehl (Harvard University, Massachusetts) at Abbey's Bookshop,
Categorical Homotopy Theory
— —
Emily Riehl (Harvard University, Massachusetts)

Categorical Homotopy Theory

Emily Riehl (Harvard University, Massachusetts)

$159.95

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English
Cambridge University Press
26 May 2014
Geometry; Topology; Algebraic topology
Series: New Mathematical Monographs
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
By:  
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Volume:   24
Dimensions:   Height: 229mm,  Width: 152mm,  Spine: 25mm
Weight:   720g
ISBN:   9781107048454
ISBN 10:   1107048451
Series:   New Mathematical Monographs
Pages:   372
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active
Part I. Derived Functors and Homotopy (Co)limits: 1. All concepts are Kan extensions; 2. Derived functors via deformations; 3. Basic concepts of enriched category theory; 4. The unreasonably effective (co)bar construction; 5. Homotopy limits and colimits: the theory; 6. Homotopy limits and colimits: the practice; Part II. Enriched Homotopy Theory: 7. Weighted limits and colimits; 8. Categorical tools for homotopy (co)limit computations; 9. Weighted homotopy limits and colimits; 10. Derived enrichment; Part III. Model Categories and Weak Factorization Systems: 11. Weak factorization systems in model categories; 12. Algebraic perspectives on the small object argument; 13. Enriched factorizations and enriched lifting properties; 14. A brief tour of Reedy category theory; Part IV. Quasi-Categories: 15. Preliminaries on quasi-categories; 16. Simplicial categories and homotopy coherence; 17. Isomorphisms in quasi-categories; 18. A sampling of 2-categorical aspects of quasi-category theory.

Emily Riehl is a Benjamin Peirce Fellow in the Department of Mathematics at Harvard University, Massachusetts and a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow.

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