  In this informal expository note, we present a universal, formulaic
construction of the free product of rigid $C^*$-2-categories. This construction
allows for a straightforward, purely categorical formulation of the free
composition of subfactors and planar algebras considered by Bisch and Jones. As
an application, we explain the results of Tarrago and Wahl on free wreath
products of compact quantum groups in this categorical language.
