Homotopy Theory of Higher Categories

English

Series: New Mathematical Monographs

ISBN: 1139180436

EAN: 9781139180436

Category: Mathematics / Group Theory/Mathematics / Topology/

Publisher: Cambridge University Press

Release Date: 10/20/2011

Synopsis: 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.

Excerpt: Unknown Property Excerpt

Homotopy Theory of Higher Categories

Illustrated: No

Format: eBook - PDF

Pages: 652