Control.Allegory

Allegories are generalizations of categories to cover relations.

Documentation

class Category k => Allegory k where

Methods

(.<=.) :: k a b -> k a b -> Bool

meet :: k a b -> k a b -> k a b

converse :: k a b -> k b a

isSimple :: k a b -> Bool

isTotal :: k a b -> Bool

isMap :: k a b -> Bool

class Allegory k => TabulatedAllegory k f where

Methods

tabulateLeft :: k a b -> k a (f a b)

tabulateRight :: k a b -> k b (f a b)

class Allegory k => UnitalAllegory k i | k -> i where

Methods

all :: k a i

rightDomain :: k b a -> k b b

leftDomain :: k b a -> k a a

class (Allegory k1, Allegory k2, CFunctor f k1 k2) => Relator f k1 k2

data Map k a b

Constructors

Map

Fields

runMap :: k a b

Instances

Allegory k => Category (Map k)

extractMap :: Allegory k => k a b -> Maybe (Map k a b)