Homotopy theory of higher categories
By: Carlos Simpson
Series: New mathematical monographs -- 19; New mathematical monographs -- 19.
Publisher: Cambridge University Press
Published: 2012
Place of publication: Cambridge; New York
Language: eng
Number of pages: 634
ISBN-13: 9780521516952
Subjects: MATHEMATICS / Topology; Categories (Mathematics); Homotopy theory
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"--
Notes: Includes bibliographical references (p. [618]-629) and index.
Table of contents: title: Part I. Higher Categories: 1. History and motivation; 2. Strict n-categories; 3. Fundamental elements of n-categories; 4. Operadic approaches; 5. Simplicial approaches; 6. Weak enrichment over a cartesian model category: an introduction; title: Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization; title: Part III. Generators and Relations: 10. Precategories; 11. Algebraic theories in model categories; 12. Weak equivalences; 13. Cofibrations; 14. Calculus of generators and relations; 15. Generators and relations for Segal categories; title: Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories; title: Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization.