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2010 A cartesian presentation of weak $n$–categories
Charles Rezk
Geom. Topol. 14(1): 521-571 (2010). DOI: 10.2140/gt.2010.14.521

Abstract

We propose a notion of weak (n+k,n)–category, which we call (n+k,n)Θ–spaces. The (n+k,n)Θ–spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal’s category Θn. This notion is a generalization of that of complete Segal spaces (which are precisely the (,1)Θ–spaces). Our main result is that the above model category is cartesian.

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Charles Rezk. "A cartesian presentation of weak $n$–categories." Geom. Topol. 14 (1) 521 - 571, 2010. https://doi.org/10.2140/gt.2010.14.521

Information

Received: 7 February 2009; Revised: 6 May 2009; Accepted: 16 September 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1203.18015
MathSciNet: MR2578310
Digital Object Identifier: 10.2140/gt.2010.14.521

Subjects:
Primary: 18D05
Secondary: 55U40

Keywords: $n$–categories , complete Segal spaces

Rights: Copyright © 2010 Mathematical Sciences Publishers

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