Data.Category.Kleisli

This is an attempt at the Kleisli category, and the construction of an adjunction for each monad.

Documentation

data Kleisli m a b where

Constructors

Kleisli :: (Functor m, Dom m ~ k, Cod m ~ k) => Monad m -> Obj k b -> k a (m :% b) -> Kleisli m a b

Instances

Category (Kleisli m)

The category of Kleisli arrows.

kleisliId :: (Functor m, Dom m ~ k, Cod m ~ k) => Monad m -> Obj k a -> Kleisli m a a

data KleisliAdjF m

Constructors

KleisliAdjF (Monad m)

Instances

(Functor m, ~ (* -> * -> *) (Dom m) k, ~ (* -> * -> *) (Cod m) k) => Functor (KleisliAdjF m)

data KleisliAdjG m

Constructors

KleisliAdjG (Monad m)

Instances

(Functor m, ~ (* -> * -> *) (Dom m) k, ~ (* -> * -> *) (Cod m) k) => Functor (KleisliAdjG m)

kleisliAdj :: (Functor m, Dom m ~ k, Cod m ~ k) => Monad m -> Adjunction (Kleisli m) k (KleisliAdjF m) (KleisliAdjG m)