Homotopy Theory of Higher Categories
Homotopy Theory of Higher Categories
£80.00
GBPThe study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
- Proposes a working theory of higher categories
- Focuses on one specific approach based closely on the work of Graeme Segal
- Useful reference to the different approaches adopted by researchers
Product details
March 2012Adobe eBook Reader
9781139180436
0 pages
0kg
35 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Prologue
- Acknowledgements
- Part I. Higher Categories:
- 1. History and motivation
- 2. Strict n-categories
- 3. Fundamental elements of n-categories
- 4. The need for weak composition
- 5. Simplicial approaches
- 6. Operadic approaches
- 7. Weak enrichment over a Cartesian model category: an introduction
- Part II. Categorical Preliminaries:
- 8. Some category theory
- 9. Model categories
- 10. Cartesian model categories
- 11. Direct left Bousfield localization
- Part III. Generators and Relations:
- 12. Precategories
- 13. Algebraic theories in model categories
- 14. Weak equivalences
- 15. Cofibrations
- 16. Calculus of generators and relations
- 17. Generators and relations for Segal categories
- Part IV. The Model Structure:
- 18. Sequentially free precategories
- 19. Products
- 20. Intervals
- 21. The model category of M-enriched precategories
- 22. Iterated higher categories
- Part V. Higher Category Theory:
- 23. Higher categorical techniques
- 24. Limits of weak enriched categories
- 25. Stabilization
- Epilogue
- References
- Index.
