Copyright	(C) 2013-2016 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	Haskell2010

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 details

Representable f => Representable (Yoneda f) Source #
Instance details Defined in Data.Functor.Contravariant.Yoneda 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 #
Contravariant (Yoneda f) Source #
Instance details Defined in Data.Functor.Contravariant.Yoneda Methods contramap :: (a' -> a) -> Yoneda f a -> Yoneda f a' # (>$) :: b -> Yoneda f b -> Yoneda f a #
Adjunction f g => Adjunction (Yoneda f) (Yoneda g) Source #
Instance details Defined in Data.Functor.Contravariant.Yoneda 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) Source #
Instance details Defined in Data.Functor.Contravariant.Yoneda type Rep (Yoneda f) = Rep f

liftYoneda . lowerYoneda ≡ id
lowerYoneda . liftYoneda ≡ id