Mario Román

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Kleisli object

Last updated May 18, 2023

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.

kleisli-in-cat

# 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.

kleisli-in-prof