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# Kleisli category

<https://bartoszmilewski.com/2014/12/23/kleisli-categories/> <https://ncatlab.org/nlab/show/Kleisli+category> <https://en.wikipedia.org/wiki/Kleisli_category>

* Kleisli category is a category naturally associated to any monad T
* Kleisli category is equivalent to the category of free T-algebras
* The Kleisli category is one of two extremal solutions to the question: does every monad arise from an adjunction? The other extremal solution is the Eilenberg-Moore category.