Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The folk model category structure on strict $\omega$-categories is
  monoidal   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.

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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph