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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.
- Sales Rank: #759699 in Books
- Published on: 2011-12-30
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x 1.50" w x 5.98" l, 2.30 pounds
- Binding: Hardcover
- 652 pages
About the Author
Carlos Simpson is Directeur de Recherche in the CNRS in Toulouse and Nice, France.
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