Geodesic
The folk model category structure on strict ω-categories is monoidal
Theory and applications of categories, Tome 35 (2020), pp. 745-808.

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We prove that the folk model category structure on the category of strict ω-categories, introduced by Lafont, Métayer and Worytkiewicz, is monoidal, first, for the Gray tensor product and, second, for the join of ω-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 ω-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.
Publié le :
Classification : 18M05, 18N30, 18N40, 55U35
Keywords: augmented directed complexes, folk model category structure, Gray tensor product, join, locally biclosed monoidal categories, monoidal model categories, oplax transformations, strict ω-categories, strict ω-groupoids, strict (m, n)-categories 
@article{TAC_2020_35_a20,
     author = {Dimitri Ara and Maxime Lucas},
     title = {The folk model category structure on strict
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     journal = {Theory and applications of categories},
     pages = {745--808},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a20/}
}
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Dimitri Ara; Maxime Lucas. The folk model category structure on strict
ω-categories is monoidal. Theory and applications of categories, Tome 35 (2020), pp. 745-808. http://geodesic.mathdoc.fr/item/TAC_2020_35_a20/