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

Viktoriya Ozornova, Martina Rovelli

Published 2018-09-27Version 1

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 $(\infty,n)$-categories. This model structure was first conjectured by Riehl to be a special case of a family of model structures due to Verity. We then construct a Quillen equivalent model based on simplicial presheaves over a category that can facilitate the comparison with other established models.