Homotopy Theory of Higher Categories: From Segal Categories to n-Categories and Beyond - New Mathematical Monographs 19 (Hardback)Carlos Simpson (author)
Hardback 652 Pages / Published: 20/10/2011
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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.
Publisher: Cambridge University Press
Number of pages: 652
Weight: 1040 g
Dimensions: 228 x 152 x 38 mm
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