Freyd is Kleisli, for Arrows
Bart Jacobs, Ichiro Hasuo · Electronic workshops in computing · 2006
Arrows have been introduced in functional programming as generalisations of monads. They also generalise comonads. Fundamental structures associated with (co)monads are Kleisli categories and categories of (Eilenberg-Moore) algebras. Hence it makes sense to ask if there are analogous structures for Arrows. In this short note we shall take first steps in this direction, and identify for instance the Freyd category that is commonly associated with an Arrow as a Kleisli category.