Re:Monads are monoids in the category of endofunctors
by Twisol on Friday September 10, 2021 @05:11AM
(#28479264)
Nice explanation! Minor nit toward the end:
> So a monoid is also a type constructor
Is it? You claimed correctly a couple paragraphs back that a functor is a type constructor F bundled with the ability to "lift" functions into the context of F. So `List` is a functor in the usual way, and so on. But a monoid cannot be a type constructor, or else `String` could not be a monoid. A monoid is a concrete type M bundled with multiplication and unit on that type.
> So a monoid is also a type constructor
Is it? You claimed correctly a couple paragraphs back that a functor is a type constructor F bundled with the ability to "lift" functions into the context of F. So `List` is a functor in the usual way, and so on. But a monoid cannot be a type constructor, or else `String` could not be a monoid. A monoid is a concrete type M bundled with multiplication and unit on that type.