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 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.

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

data ForgetMonoid

Constructors

ForgetMonoid

Instances

Functor ForgetMonoid

data FreeMonoid

Constructors

FreeMonoid

Instances

Functor FreeMonoid

freeMonoidAdj :: Adjunction Mon (->) FreeMonoid ForgetMonoid

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

listMonadReturn :: a -> [a]

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

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

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