15 Jul
2007
15 Jul
'07
3:25 a.m.
SOR> I've heard that Monads are in some way like Monoids, hence the SOR> name. But I don't understand the explanation yet myself :( Just compare: Monoid: a set M with maps ident: M^0 -> M and product: M^2 -> M (here M^0 is a one-element set) Monad: a functor M with natural transformations return: M^0 -> M and join: M^2 -> M (here M^0 is an identity functor) If you extend the definition of monoid to arbitrary "monoidal category", which means, arbitrary category with identity object I and bifunctor "\times", such that I \times X ~ X \times I ~ X and (X \times Y) \times Z ~ X \times (Y \times Z), and then apply it to the category of endofunctors with identity functor as I and composition as \times, then you get a monad.