Control.Functor.Composition.Adjoint

Documentation

class (Covariant t, Covariant u) => Adjoint t u | t -> u, u -> t where

When providing a new instance, you should ensure it satisfies the four laws:
* Left adjunction identity: phi counit ≡ identity
* Right adjunction identity: psi unit ≡ identity
* Left adjunction interchange: phi f ≡ comap f . eta
* Right adjunction interchange: psi f ≡ epsilon . comap f

Minimal complete definition

phi, psi

Methods

phi :: (t a -> b) -> a -> u b

Left adjunction

psi :: (a -> u b) -> t a -> b

Right adjunction

eta :: a -> (u :.: t) a

epsilon :: (t :.: u) a -> a

type (-|) = Adjoint