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"Homotopy theory of higher categories" was published by Cambridge University Press in 2012 - Cambridge, it has 634 pages and the language of the book is English.


“Homotopy theory of higher categories” Metadata:

  • Title: ➤  Homotopy theory of higher categories
  • Author:
  • Language: English
  • Number of Pages: 634
  • Publisher: Cambridge University Press
  • Publish Date:
  • Publish Location: Cambridge

“Homotopy theory of higher categories” Subjects and Themes:

Edition Specifications:

  • Pagination: xviii, 634 p. :

Edition Identifiers:

AI-generated Review of “Homotopy theory of higher categories”:


"Homotopy theory of higher categories" Table Of Contents:

  • 1- 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
  • 2- Part II. Categorical Preliminaries: 7. Model categories; 8. Cell complexes in locally presentable categories; 9. Direct left Bousfield localization
  • 3- 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
  • 4- Part IV. The Model Structure: 186 Sequentially free precategories; 17. Products; 18. Intervals; 19. The model category of M-enriched precategories
  • 5- Part V. Higher Category Theory: 20. Iterated higher categories; 21. Higher categorical techniques; 22. Limits of weak enriched categories; 23. Stabilization.

"Homotopy theory of higher categories" Description:

The Open Library:

"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"--

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