#
The folk model category structure on strict
ω-categories is monoidal

##
Dimitri Ara and Maxime Lucas

We prove that the folk model category structure on the category of strict
ω-categories, introduced by Lafont, MÃ©tayer 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.

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

2020 MSC:
18M05, 18N30, 18N40, 55U35

*Theory and Applications of Categories,*
Vol. 35, 2020,
No. 21, pp 745-808.

Published 2020-05-28.

http://www.tac.mta.ca/tac/volumes/35/21/35-21.pdf

TAC Home