Data.Functor.Contravariant.Yoneda

Documentation

newtype Yoneda f a

Yoneda embedding for a presheaf

Constructors

Yoneda

Fields

• runYoneda :: forall r. (r -> a) -> f r

Instances

Contravariant (Yoneda f)

Methods

contramap :: (a -> b) -> Yoneda f b -> Yoneda f a

(>$) :: b -> Yoneda f b -> Yoneda f a

Representable f => Representable (Yoneda f)

Associated Types

type Rep (Yoneda f :: * -> *) :: *

Methods

tabulate :: (a -> Rep (Yoneda f)) -> Yoneda f a

index :: Yoneda f a -> a -> Rep (Yoneda f)

contramapWithRep :: (b -> Either a (Rep (Yoneda f))) -> Yoneda f a -> Yoneda f b

Adjunction f g => Adjunction (Yoneda f) (Yoneda g)

Methods

unit :: a -> Yoneda g (Yoneda f a)

counit :: a -> Yoneda f (Yoneda g a)

leftAdjunct :: (b -> Yoneda f a) -> a -> Yoneda g b

rightAdjunct :: (a -> Yoneda g b) -> b -> Yoneda f a

type Rep (Yoneda f)

type Rep (Yoneda f) = Rep f

liftYoneda :: Contravariant f => f a -> Yoneda f a

liftYoneda . lowerYoneda ≡ id
lowerYoneda . liftYoneda ≡ id

lowerYoneda :: Yoneda f a -> f a