#### Volume 14, issue 1 (2010)

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A cartesian presentation of weak $n$–categories

### Charles Rezk

Geometry & Topology 14 (2010) 521–571
##### Abstract

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.

##### Keywords
$n$–categories, complete Segal spaces
Primary: 18D05
Secondary: 55U40