The Gray tensor product for 2-quasi-categories

Abstract

We construct an $(\infty ,2)$-version of the (lax) Gray tensor product. On the 1-categorical level, this is a binary (or more generally an $n$-ary) functor on the category of ${\Theta }_2$-sets, and it is shown to be left Quillen with respect to Ara's model structure. Moreover we prove that this tensor product forms part of a "homotopical" (biclosed) monoidal structure, or more precisely a normal lax monoidal structure that is associative up to homotopy.

v3: 63 pages. Minor revision. Published version

References in corpus (1)

• A homotopy coherent cellular nerve for bicategories

Cited by in corpus (4)

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• A cubical model for $(\infty ,n)$-categories