>>18
A monoid is...
* A set, S
* An operation, • : S × S -> S
* An element of S, e : 1 -> S
...satisfying these laws:
* (a • b) • c = a • (b • c), for all a, b and c in S
* e • a = a = a • e, for all a in S
A monad is...
* An endofunctor, T : X -> X
* A natural transformation, μ : T × T -> T, where × means functor composition
* A natural transformation, η : I -> T, where I is the identity endofunctor on X
...satisfying these laws:
* μ(μ(T × T) × T)) = μ(T × μ(T × T))
* μ(η(T)) = T = μ(T(η))