  Various monoidal categories, including suitable representation categories of
vertex operator algebras, admit natural Grothendieck-Verdier duality
structures. We recall that such a Grothendieck-Verdier category comes with two
tensor products which should be related by distributors obeying pentagon
identities. We discuss in which circumstances these distributors are
isomorphisms. This is achieved by taking the perspective of module categories
over monoidal categories, using in particular the natural weak module functor
structure of internal Homs and internal coHoms. As an illustration, we exhibit
these concepts concretely in the case of categories of bimodules over
associative algebras.
