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

TL;DR

This paper establishes a new model structure for $( abla,n)$-categories using stratified simplicial sets, providing a framework that aligns with existing models and facilitates comparisons.

Contribution

It introduces a novel model structure for $( abla,n)$-categories on stratified simplicial sets and constructs a Quillen equivalent model for better comparison with other models.

Findings

Existence of a model structure with $n$-complicial sets as fibrant objects.

Construction of a Quillen equivalent model based on simplicial presheaves.

Facilitation of comparisons with other established models.

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 $(\infty,n)$-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.