#### Volume 20, issue 3 (2020)

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

### Viktoriya Ozornova and Martina Rovelli

Algebraic & Geometric Topology 20 (2020) 1543–1600
##### 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.

##### Keywords
stratified simplicial sets, complicial sets, $(\infty,n)$–categories, model categories
##### Mathematical Subject Classification 2010
Primary: 18D05, 55U10, 55U35