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Categorical Homotopy Theory

emily Riehl
Publisher: 
Cambridge University Press
Publication Date: 
2014
Number of Pages: 
352
Format: 
Hardcover
Series: 
New Mathematical Monographs 24
Price: 
99.00
ISBN: 
9781107048454
Category: 
Monograph
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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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