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.
ASJC Scopus subject areas
- Geometry and Topology