Given 2-categories C and D, let Lax (C,D) denote the 2-category of lax functors, lax natural transformations and modifications, and [C,D]_lnt its full sub-2-category of (strict) 2-functors. We give two isomorphic constructions of a 2-category C \boxtimes D satisfying Lax (C, Lax(D,E)) \cong [C \boxtimes D, E}_lnt, hence generalising the case of the free distributive law 1 \boxtimes 1. We also discuss dual constructions.
Keywords: Lax functor, strictification, distributive law, lax Gray product, free monoid
2010 MSC: 18D05, 18D35, 18G30
Theory and Applications of Categories, Vol. 34, 2019, No. 22, pp 635-661.