The Gray tensor product for 2-quasi-categories

Abstract

We construct an (∞, 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 Θ 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" monoidal (closed) structure, or more precisely a normal lax monoidal structure that is associative up to homotopy.