A cartesian presentation of weak n-categories

Understand

We propose a notion of weak (n+k,n)-category, which we call (n+k,n)-Theta-spaces.

• The (n+k,n)-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 (infty,1)-Theta-spaces).
• Our main result is that the above model category is cartesian.