Data.Category.Monoid

A monoid as a category with one object.

Documentation

data MonoidA m a b where

The arrows are the values of the monoid.

Constructors

MonoidA :: Monoid m => m -> MonoidA m m m

Instances

Monoid m => Category (MonoidA m)

A (prelude) monoid as a category with one object.

data Mon where

Constructors

MonoidMorphism :: (Monoid m1, Monoid m2) => (m1 -> m2) -> Mon m1 m2

Instances

Category Mon

The category of all monoids, with monoid morphisms as arrows.

data ForgetMonoid

Constructors

ForgetMonoid

Instances

Functor ForgetMonoid

The ForgetMonoid functor forgets the monoid structure.

data FreeMonoid

Constructors

FreeMonoid

Instances

Functor FreeMonoid

The FreeMonoid functor is the list functor.

freeMonoidAdj :: Adjunction Mon (->) FreeMonoid ForgetMonoid

The free monoid functor is left adjoint to the forgetful functor.

foldMap :: Monoid m => (a -> m) -> [a] -> m

listMonadReturn :: a -> [a]

listMonadJoin :: [[a]] -> [a]

listComonadExtract :: Monoid m => [m] -> m

listComonadDuplicate :: Monoid m => [m] -> [[m]]