Homotopy Theory of Higher Categories

Homotopy Theory of Higher Categories

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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.From Segal Categories to n-Categories and Beyond Carlos Simpson. pf alt;Ac}a#39;lA, -) : p;?A, - and pAsa€œ(pf) 1 pAsa€œ(A, -) 4 p;7Aj provide the transition maps for the system of pf (A, -) considered as a diagram oz 4anbsp;...

Title:Homotopy Theory of Higher Categories
Author:Carlos Simpson
Publisher:Cambridge University Press - 2011-10-20


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