Homotopy theory of higher categories
Author(s)
Bibliographic Information
Homotopy theory of higher categories
(New mathematical monographs, 19)
Cambridge University Press, 2012
- Other Title
-
From segal categories to n-categories and beyond
Available at 20 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
SIM||32||1200021323570
Note
Includes bibliographical references and index
Description and Table of Contents
Description
The 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.
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.
by "Nielsen BookData"