Algebras are promonads

You’ve probably heard the slogan that “a monad is a monoid in a category of endofunctors.” By analogy, a promonad is a monoid in a category of endoprofunctors. Or, if you prefer, a promonad is a monad in the bicategory of profunctors.1 I found myself thinking about promonads recently, for reasons that I will reveal in the fullness of time.

This is a companion discussion topic for the original entry at