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arXiv · 2106.09428

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

Brandon Doherty·Chris Kapulkin·Yuki Maehara
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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.

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Brandon Doherty, Chris Kapulkin, Yuki Maehara. 2021-06-17. Equivalence of cubical and simplicial approaches to $(\infty,n)$-categories. https://arxiv.org/abs/2106.09428

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