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 $(\infty ,n)$-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.

Final version

References in corpus (1)

• On the equivalence between ${\Theta }_n$-spaces and iterated Segal spaces

Cited by in corpus (4)

• An $(\infty ,2)$-categorical pasting theorem
• Orientals as free weak $\omega$-categories
• Nerves and cones of free loop-free ω-categories
• Discreteness and completeness for ${\Theta }_n$-models of $(\infty ,n)$-categories