Model structures for .1; n/–categories on (pre)stratified simplicial sets and prestratified simplicial spaces

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 .1; n/–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.