Tags: bicategory, Bimodule on a bicategory, monoid, Module, drawing universal modules. References.
In the bicategory of categories
Proposition. In CAT, the bicategory of categories, the Kleisli object of a monad is the category of free algebras.
In the bicategory of profunctors
Proposition. In PROF, the bicategory of profunctors, the Kleisli object of a promonad is the category with morphisms in the promonad.
