Equivalence of cubical and simplicial approaches to $(\infty ,n)$-categories

Abstract

We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for ($n$-trivial, saturated) comical sets to the category of marked simplicial set equipped with a model structure for ($n$-trivial, saturated) complicial sets is a Quillen equivalence. Our proof is based on the theory of cones, previously developed by the first two authors together with Lindsey and Sattler.

arXiv commentversion accepted for publication

References in corpus (2)

• The Gray tensor product for 2-quasi-categories
• Cubical models of $(\infty ,1)$-categories

Cited by in corpus (1)

• Yoneda Lemma for $\mathcal{D}$-Simplicial Spaces