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?


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