Kleisli object

Last updated May 18, 2023

Tags: Bicategory, Bimodule on a bicategory, Monoid, Module. References.

• The Formal Theory of Monads (Street, 1972)

Proposition. In CAT, the bicategory of categories, the Kleisli object of a monad is the category of free algebras.

Proposition. In PROF, the bicategory of profunctors, the Kleisli object of a promonad is the category with morphisms in the promonad.