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

Contravariant ( Yoneda f) Source #
Instance details Defined in Data.Functor.Contravariant.Yoneda Methods contramap :: (a -> b) -> Yoneda f b -> Yoneda f a Source # (>$) :: b -> Yoneda f b -> Yoneda f a Source #
Representable f => Representable ( Yoneda f) Source #
Instance details Defined in Data.Functor.Contravariant.Yoneda Associated Types type Rep ( Yoneda f) Source # Methods tabulate :: (a -> Rep ( Yoneda f)) -> Yoneda f a Source # index :: Yoneda f a -> a -> Rep ( Yoneda f) Source # contramapWithRep :: (b -> Either a ( Rep ( Yoneda f))) -> Yoneda f a -> Yoneda f b Source #
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) Source # counit :: a -> Yoneda f ( Yoneda g a) Source # leftAdjunct :: (b -> Yoneda f a) -> a -> Yoneda g b Source # rightAdjunct :: (a -> Yoneda g b) -> b -> Yoneda f a Source #
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