We reinvented Monads!

A monad is a triplet (M,⊙,η) where

• \(M\) an Endofunctor (to type a associate M a)
• \(⊙:M×M→M\) a nat. trans. (i.e. ⊙::M (M a) → M a ; join)
• \(η:I→M\) a nat. trans. (\(I\) identity functor ; η::a → M a)

Satisfying

• \(M ⊙ (M ⊙ M) = (M ⊙ M) ⊙ M\)
• \(η ⊙ M = M = M ⊙ η\)