A pseudomonoid is defined within a monoidal bicategory. It is like a monoid in a monoidal category except that the usual axioms hold up to coherent invertible 2-cells. Pseudomonoid is like a monoidal category, which is its example.
Pseudomodule, or a pseudo-actee for a pseudomonoid consists of an object on which the pseudomonoid acts, with the action axioms satisfied up to coherent invertible 2-cells. Has anyone seen such pseudomodules or similar notions such as a monoidal category-actee?
And a more general question:
Coherence for pseudomodules can be quite obviously understood in the "all diagrams commute" way. I believe that finitary coherence axioms follow from known coherence theorems. In fact coherence axioms for a pseudomonoid itself should also follow from these. However I can not think of a result in a widely known literature that would be readily applicable to situations as such. Does such a theorem exist?