Copyright	(C) 2013 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	GADTs, TFs, MPTCs
Safe Haskell	Trustworthy
Language	Haskell98

Data.Functor.Contravariant.Yoneda

Description

Synopsis

Documentation

newtype Yoneda f a Source

Yoneda embedding for a presheaf

Constructors

Yoneda
Fields runYoneda :: forall r. (r -> a) -> f r

Instances

Contravariant (Yoneda f) Source
Methods contramap :: (a -> b) -> Yoneda f b -> Yoneda f a (>$) :: b -> Yoneda f b -> Yoneda f a
Representable f => Representable (Yoneda f) Source
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) Source
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) = Rep f Source

liftYoneda . lowerYoneda ≡ id
lowerYoneda . liftYoneda ≡ id