We propose a notion of weak –category, which we call ––spaces. The ––spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal’s category . This notion is a generalization of that of complete Segal spaces (which are precisely the ––spaces). Our main result is that the above model category is cartesian.
"A cartesian presentation of weak $n$–categories." Geom. Topol. 14 (1) 521 - 571, 2010. https://doi.org/10.2140/gt.2010.14.521