Equivalence of cubical and simplicial approaches to (∞,n)-categories

2021/06/17 by Brandon Doherty, Doherty, Brandon, Chris Kapulkin +3 · 1 citation
Mathematics · #18N65 #55U35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2106.09428

openalex publication_date 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Cubical models of (∞, 1)-categories

Cited by

• On the squares functor and the Gaitsgory-Rozenblyum conjectures

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