Model structures for $(\infty,n)$–categories on (pre)stratified simplicial sets and prestratified simplicial spaces

Abstract

We prove the existence of a model structure on the category of stratified simplicial sets whose fibrant objects are precisely $n$–complicial sets, which are a proposed model for $\left(\infty ,n\right)$–categories, based on previous work of Verity and Riehl. We then construct a Quillen equivalent model based on simplicial presheaves over a category that can facilitate the comparison with other established models.