Copyright	Guillaume Sabbagh 2021
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

OppositeCategory.OppositeCategory

Description

The opposite of a category is a category with reversed arrows.

Synopsis

data OppositeMorphism m o = OpMorph m
data OppositeCategory c m o = Op c
opOpMorph :: OppositeMorphism m o -> m
opOp :: OppositeCategory c m o -> c

Documentation

data OppositeMorphism m o Source #

Morphism in an opposite category.

Constructors

OpMorph m

Instances

Instances details

Eq m => Eq (OppositeMorphism m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods (==) :: OppositeMorphism m o -> OppositeMorphism m o -> Bool (/=) :: OppositeMorphism m o -> OppositeMorphism m o -> Bool
Ord m => Ord (OppositeMorphism m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods compare :: OppositeMorphism m o -> OppositeMorphism m o -> Ordering (<) :: OppositeMorphism m o -> OppositeMorphism m o -> Bool (<=) :: OppositeMorphism m o -> OppositeMorphism m o -> Bool (>) :: OppositeMorphism m o -> OppositeMorphism m o -> Bool (>=) :: OppositeMorphism m o -> OppositeMorphism m o -> Bool max :: OppositeMorphism m o -> OppositeMorphism m o -> OppositeMorphism m o min :: OppositeMorphism m o -> OppositeMorphism m o -> OppositeMorphism m o
Show m => Show (OppositeMorphism m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods showsPrec :: Int -> OppositeMorphism m o -> ShowS show :: OppositeMorphism m o -> String showList :: [OppositeMorphism m o] -> ShowS
PrettyPrintable m => PrettyPrintable (OppositeMorphism m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods pprint :: OppositeMorphism m o -> String Source #
Morphism m o => Morphism (OppositeMorphism m o) o Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods (@) :: OppositeMorphism m o -> OppositeMorphism m o -> OppositeMorphism m o Source # source :: OppositeMorphism m o -> o Source # target :: OppositeMorphism m o -> o Source #
(GeneratedFiniteCategory c m o, Morphism m o) => GeneratedFiniteCategory (OppositeCategory c m o) (OppositeMorphism m o) o Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods genAr :: OppositeCategory c m o -> o -> o -> [OppositeMorphism m o] Source # decompose :: OppositeCategory c m o -> OppositeMorphism m o -> [OppositeMorphism m o] Source # genArrows :: OppositeCategory c m o -> [OppositeMorphism m o] Source #
(FiniteCategory c m o, Morphism m o) => FiniteCategory (OppositeCategory c m o) (OppositeMorphism m o) o Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods ob :: OppositeCategory c m o -> [o] Source # identity :: OppositeCategory c m o -> o -> OppositeMorphism m o Source # ar :: OppositeCategory c m o -> o -> o -> [OppositeMorphism m o] Source # arrows :: OppositeCategory c m o -> [OppositeMorphism m o] Source #

data OppositeCategory c m o Source #

Opposite category of a given category.

Constructors

Op c

Instances

Instances details

Eq c => Eq (OppositeCategory c m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods (==) :: OppositeCategory c m o -> OppositeCategory c m o -> Bool (/=) :: OppositeCategory c m o -> OppositeCategory c m o -> Bool
Ord c => Ord (OppositeCategory c m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods compare :: OppositeCategory c m o -> OppositeCategory c m o -> Ordering (<) :: OppositeCategory c m o -> OppositeCategory c m o -> Bool (<=) :: OppositeCategory c m o -> OppositeCategory c m o -> Bool (>) :: OppositeCategory c m o -> OppositeCategory c m o -> Bool (>=) :: OppositeCategory c m o -> OppositeCategory c m o -> Bool max :: OppositeCategory c m o -> OppositeCategory c m o -> OppositeCategory c m o min :: OppositeCategory c m o -> OppositeCategory c m o -> OppositeCategory c m o
Show c => Show (OppositeCategory c m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods showsPrec :: Int -> OppositeCategory c m o -> ShowS show :: OppositeCategory c m o -> String showList :: [OppositeCategory c m o] -> ShowS
PrettyPrintable c => PrettyPrintable (OppositeCategory c m o) Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods pprint :: OppositeCategory c m o -> String Source #
(GeneratedFiniteCategory c m o, Morphism m o) => GeneratedFiniteCategory (OppositeCategory c m o) (OppositeMorphism m o) o Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods genAr :: OppositeCategory c m o -> o -> o -> [OppositeMorphism m o] Source # decompose :: OppositeCategory c m o -> OppositeMorphism m o -> [OppositeMorphism m o] Source # genArrows :: OppositeCategory c m o -> [OppositeMorphism m o] Source #
(FiniteCategory c m o, Morphism m o) => FiniteCategory (OppositeCategory c m o) (OppositeMorphism m o) o Source #
Instance details Defined in OppositeCategory.OppositeCategory Methods ob :: OppositeCategory c m o -> [o] Source # identity :: OppositeCategory c m o -> o -> OppositeMorphism m o Source # ar :: OppositeCategory c m o -> o -> o -> [OppositeMorphism m o] Source # arrows :: OppositeCategory c m o -> [OppositeMorphism m o] Source #

opOpMorph :: OppositeMorphism m o -> m Source #

Transforms back an opposite morphism into the original morphism.

opOp :: OppositeCategory c m o -> c Source #

Transforms an opposite category into the original category.