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


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.


Download Citation

Charles Rezk. "A cartesian presentation of weak $n$–categories." Geom. Topol. 14 (1) 521 - 571, 2010.


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

Primary: 18D05
Secondary: 55U40

Keywords: $n$–categories , complete Segal spaces

Rights: Copyright © 2010 Mathematical Sciences Publishers

Vol.14 • No. 1 • 2010
Back to Top