  Given 2-categories $\mathcal{C}$ and $\mathcal{D}$, let
$\textrm{Lax}(\mathcal{C},\mathcal{D})$ denote the 2-category of lax functors,
lax natural transformations and modifications, and
$[\mathcal{C},\mathcal{D}]_\mathrm{lnt}$ its full sub-2-category of (strict)
2-functors. We give two isomorphic constructions of a 2-category
$\mathcal{C}\boxtimes\mathcal{D}$ satisfying
$\textrm{Lax}(\mathcal{C},\textrm{Lax}(\mathcal{D},\mathcal{E})) \cong
[\mathcal{C}\boxtimes \mathcal{D},\mathcal{E}]_\mathrm{lnt}$, hence
generalising the case of the free distributive law $1\boxtimes 1$. We also
discuss dual constructions.

Category Theory