Description

Book Synopsis
This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

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.

Categorical Homotopy Theory 24 New Mathematical Monographs Series Number 24

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    A Hardback by Emily Riehl

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      View other formats and editions of Categorical Homotopy Theory 24 New Mathematical Monographs Series Number 24 by Emily Riehl

      Publisher: Cambridge University Press
      Publication Date: Publication Date: 5/26/2014 12:00:00 AM
      ISBN13: 9781107048454, 978-1107048454
      ISBN10: 1107048451
      Also in:
      Geometry

      Description

      Book Synopsis
      This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

      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.

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