Mario Román


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Kleisli object

Last updated Oct 31, 2023


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.