Equivalence of cubical and simplicial approaches to $(\infty,n)$-categories
Algebraic Topology
2025-12-23 v4 Category Theory
Abstract
We prove that the marked triangulation functor from the category of marked cubical sets equipped with a model structure for (-trivial, saturated) comical sets to the category of marked simplicial set equipped with a model structure for (-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.
Keywords
Cite
@article{arxiv.2106.09428,
title = {Equivalence of cubical and simplicial approaches to $(\infty,n)$-categories},
author = {Brandon Doherty and Chris Kapulkin and Yuki Maehara},
journal= {arXiv preprint arXiv:2106.09428},
year = {2025}
}
Comments
version accepted for publication