Kleisli object
Tags: Bicategory, Bimodule on a bicategory, Monoid, Module. 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.