Homotopy theory of higher categories
QA612.7 .S56 2012
- Unknown QA612.7 .S56 2012
- Includes bibliographical references (p. -629) and index.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
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- Carlos Simpson.
- New mathematical monographs ; 19