Categorical Homotopy Theory by Emily Riehl (English) Hardcover Book

Description: Categorical Homotopy Theory by Emily Riehl This categorical perspective on homotopy theory helps consolidate and simplify ones understanding of derived functors, homotopy limits and colimits, and model categories, among others. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 - Quillens 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. Author Biography 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. Table of Contents 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. Promotional "Headline" This categorical perspective on homotopy theory helps consolidate and simplify ones understanding of derived functors, homotopy limits and colimits, and model categories, among others. Description for Bookstore A typical proposition in homotopy theory asserts that two objects are weakly equivalent. But sometimes this statement obscures a more precise truth: that particular models for the relevant objects are isomorphic. This book, with its focus on enriched category theory, helps tease apart the categorical statements (asserting isomorphism) from the essentially homotopical ones (asserting weak equivalence). Description for Library A typical proposition in homotopy theory asserts that two objects are weakly equivalent. But sometimes this statement obscures a more precise truth: that particular models for the relevant objects are isomorphic. This book, with its focus on enriched category theory, helps tease apart the categorical statements (asserting isomorphism) from the essentially homotopical ones (asserting weak equivalence). Details ISBN1107048451 Author Emily Riehl Publisher Cambridge University Press Series New Mathematical Monographs Year 2014 ISBN-10 1107048451 ISBN-13 9781107048454 Format Hardcover Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom DEWEY 514.24 Media Book Publication Date 2014-05-26 Short Title CATEGORICAL HOMOTOPY THEORY Language English Series Number 24 Pages 372 Affiliation Harvard University, Massachusetts Audience Professional and Scholarly UK Release Date 2014-05-26 AU Release Date 2014-05-26 NZ Release Date 2014-05-26 Illustrations Worked examples or Exercises We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:168628434;

Price: 227.08 AUD

Location: Melbourne

End Time: 2025-01-24T06:04:33.000Z

Shipping Cost: 12.7 AUD