Homotopy Theory of Higher Categories: From Segal Categories to N-Categories and Beyond (Hardcover) (ISBN-13: 9780521516952)

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.

Author: Carlos Simpson
ISBN-10: 0521516951
ISBN-13: 9780521516952
Publisher: Cambridge University Press
Language: English
Published: 10/20/2011
Pages: 652
Format: Hardcover
Weight: 2.30lbs
Size: 9.10h x 6.10w x 1.50d