kan-extensions-4.2.2: Kan extensions, Kan lifts, various forms of the Yoneda lemma, and (co)density (co)monads

Copyright(C) 2013 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
PortabilityGADTs, TFs, MPTCs
Safe HaskellTrustworthy
LanguageHaskell98

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.

http://ncatlab.org/nlab/show/Yoneda+reduction

Constructors

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

liftCoyoneda :: f a -> Coyoneda f a Source

Coyoneda "expansion" of a presheaf

liftCoyoneda . lowerCoyonedaid
lowerCoyoneda . liftCoyonedaid

lowerCoyoneda :: Contravariant f => Coyoneda f a -> f a Source

Coyoneda reduction on a presheaf