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.Coyoneda

Description

The co-Yoneda lemma for presheafs states that f is naturally isomorphic to Coyoneda f.

Synopsis

Documentation

data Coyoneda f a where Source

A Contravariant functor (aka presheaf) suitable for Yoneda reduction.

Constructors

Coyoneda :: (a -> b) -> f b -> Coyoneda f a

Instances

Contravariant (Coyoneda f) Source
Methods contramap :: (a -> b) -> Coyoneda f b -> Coyoneda f a (>$) :: b -> Coyoneda f b -> Coyoneda f a
Representable f => Representable (Coyoneda f) Source
Associated Types type Rep (Coyoneda f :: * -> ) :: Methods tabulate :: (a -> Rep (Coyoneda f)) -> Coyoneda f a index :: Coyoneda f a -> a -> Rep (Coyoneda f) contramapWithRep :: (b -> Either a (Rep (Coyoneda f))) -> Coyoneda f a -> Coyoneda f b
Adjunction f g => Adjunction (Coyoneda f) (Coyoneda g) Source
Methods unit :: a -> Coyoneda g (Coyoneda f a) counit :: a -> Coyoneda f (Coyoneda g a) leftAdjunct :: (b -> Coyoneda f a) -> a -> Coyoneda g b rightAdjunct :: (a -> Coyoneda g b) -> b -> Coyoneda f a
type Rep (Coyoneda f) = Rep f Source

Coyoneda "expansion" of a presheaf

liftCoyoneda . lowerCoyoneda ≡ id
lowerCoyoneda . liftCoyoneda ≡ id

Coyoneda reduction on a presheaf