Strong promonad
Correspondence with effectful categories. Strong promonads may be read as Arrows (Hughes), or effectful categories, which particularize into Freyd categories when the base is cartesian. There is a one-to-one correspondence between strong promonads and locally small effectful categories (Heunen, Jacobs; Theorem 5.4).
References
- Generalising Monads to Arrows (Hughes)
- Arrows, like Monads, are Monoids (Heunen, Jacobs)
- Promonads and String Diagrams for Effectful Categories (Roman, 2022)
Tags: promonad, effectful category, Old - Definition of strong promonad, Strong profunctor