| Homotopy Theory of Higher Categories: From Segal Categories to N-Categories and Beyond Contributor(s): Simpson, Carlos (Author) |
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ISBN: 0511978111 ISBN-13: 9780511978111 Publisher: Cambridge University Press OUR PRICE: $140.25 Product Type: Open Ebook - Other Formats Published: October 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General |
| Dewey: 514.24 |
| Series: New Mathematical Monographs |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
Contributor Bio(s): Simpson, Carlos: - Carlos Simpson is Directeur de Recherche in the CNRS in Toulouse and Nice, France. |