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Journal Articles Theory and Applications of Categories Year : 2020

The folk model category structure on strict $\omega$-categories is monoidal

Abstract

We prove that the folk model category structure on the category of strict $\omega$-categories, introduced by Lafont, M\'etayer and Worytkiewicz, is monoidal, first, for the Gray tensor product and, second, for the join of $\omega$-categories, introduced by the first author and Maltsiniotis. We moreover show that the Gray tensor product induces, by adjunction, a tensor product of strict $(m,n)$-categories and that this tensor product is also compatible with the folk model category structure. In particular, we get a monoidal model category structure on the category of strict $\omega$-groupoids. We prove that this monoidal model category structure satisfies the monoid axiom, so that the category of Gray monoids, studied by the second author, bears a natural model category structure.

Dates and versions

hal-02386617 , version 1 (29-11-2019)

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Dimitri Ara, Maxime Lucas. The folk model category structure on strict $\omega$-categories is monoidal. Theory and Applications of Categories, 2020, 35 (21), pp.745-808. ⟨hal-02386617⟩
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