A cartesian presentation of weak n–categories

Rezk, Charles¹

¹ Department of Mathematics, University of Illinois at Urbana-Champaign, 273 Altgeld Hall, MC-382, 1409 W Green Street, Urbana, IL 61801

Geometry & topology, Tome 14 (2010) no. 1, pp. 521-571.

Résumé

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

Détail

DOI : 10.2140/gt.2010.14.521

Keywords: $n$–categories, complete Segal spaces

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