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.

Develops a full set of homotopical algebra techniques dedicated to the study of higher categories.

About the Author
Carlos Simpson is Directeur de Recherche in the CNRS in Toulouse and Nice, France.


Book Information
ISBN 9780521516952
Author Carlos Simpson
Format Hardback
Page Count 652
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 1050g
Dimensions(mm) 235mm * 158mm * 38mm