Copyright	Guillaume Sabbagh 2022
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.Categories.Opposite

Description

Each Category has an opposite one where morphisms are reversed.

Synopsis

data OpMorphism m = OpMorphism m
opOpMorphism :: OpMorphism m -> m
data Op c = Op c
opOp :: Op c -> c

Documentation

data OpMorphism m Source #

An OpMorphism is a morphism where source and target are reversed.

Constructors

OpMorphism m

Instances

Instances details

PrettyPrint m => PrettyPrint (OpMorphism m) Source #
Instance details Defined in Math.Categories.Opposite Methods pprint :: Int -> OpMorphism m -> String Source # pprintWithIndentations :: Int -> Int -> String -> OpMorphism m -> String Source # pprintIndent :: Int -> OpMorphism m -> String Source #
Simplifiable m => Simplifiable (OpMorphism m) Source #
Instance details Defined in Math.Categories.Opposite Methods simplify :: OpMorphism m -> OpMorphism m #
Generic (OpMorphism m) Source #
Instance details Defined in Math.Categories.Opposite Associated Types type Rep (OpMorphism m) :: Type -> Type Methods from :: OpMorphism m -> Rep (OpMorphism m) x to :: Rep (OpMorphism m) x -> OpMorphism m
Show m => Show (OpMorphism m) Source #
Instance details Defined in Math.Categories.Opposite Methods showsPrec :: Int -> OpMorphism m -> ShowS show :: OpMorphism m -> String showList :: [OpMorphism m] -> ShowS
Eq m => Eq (OpMorphism m) Source #
Instance details Defined in Math.Categories.Opposite Methods (==) :: OpMorphism m -> OpMorphism m -> Bool (/=) :: OpMorphism m -> OpMorphism m -> Bool
Morphism m o => Morphism (OpMorphism m) o Source #
Instance details Defined in Math.Categories.Opposite Methods (@) :: OpMorphism m -> OpMorphism m -> OpMorphism m Source # (@?) :: OpMorphism m -> OpMorphism m -> Maybe (OpMorphism m) Source # source :: OpMorphism m -> o Source # target :: OpMorphism m -> o Source #
(Category c m o, Morphism m o) => Category (Op c) (OpMorphism m) o Source #
Instance details Defined in Math.Categories.Opposite Methods identity :: Op c -> o -> OpMorphism m Source # ar :: Op c -> o -> o -> Set (OpMorphism m) Source # genAr :: Op c -> o -> o -> Set (OpMorphism m) Source # decompose :: Op c -> OpMorphism m -> [OpMorphism m] Source #
(FiniteCategory c m o, Morphism m o) => FiniteCategory (Op c) (OpMorphism m) o Source #
Instance details Defined in Math.Categories.Opposite Methods ob :: Op c -> Set o Source #
type Rep (OpMorphism m) Source #
Instance details Defined in Math.Categories.Opposite type Rep (OpMorphism m) = D1 ('MetaData "OpMorphism" "Math.Categories.Opposite" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "OpMorphism" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))

opOpMorphism :: OpMorphism m -> m Source #

Return the original morphism given an OpMorphism.

data Op c Source #

The Op operator gives the opposite of a Category.

Constructors

Op c

Instances

Instances details

PrettyPrint c => PrettyPrint (Op c) Source #
Instance details Defined in Math.Categories.Opposite Methods pprint :: Int -> Op c -> String Source # pprintWithIndentations :: Int -> Int -> String -> Op c -> String Source # pprintIndent :: Int -> Op c -> String Source #
Simplifiable c => Simplifiable (Op c) Source #
Instance details Defined in Math.Categories.Opposite Methods simplify :: Op c -> Op c #
Generic (Op c) Source #
Instance details Defined in Math.Categories.Opposite Associated Types type Rep (Op c) :: Type -> Type Methods from :: Op c -> Rep (Op c) x to :: Rep (Op c) x -> Op c
Show c => Show (Op c) Source #
Instance details Defined in Math.Categories.Opposite Methods showsPrec :: Int -> Op c -> ShowS show :: Op c -> String showList :: [Op c] -> ShowS
Eq c => Eq (Op c) Source #
Instance details Defined in Math.Categories.Opposite Methods (==) :: Op c -> Op c -> Bool (/=) :: Op c -> Op c -> Bool
(Category c m o, Morphism m o) => Category (Op c) (OpMorphism m) o Source #
Instance details Defined in Math.Categories.Opposite Methods identity :: Op c -> o -> OpMorphism m Source # ar :: Op c -> o -> o -> Set (OpMorphism m) Source # genAr :: Op c -> o -> o -> Set (OpMorphism m) Source # decompose :: Op c -> OpMorphism m -> [OpMorphism m] Source #
(FiniteCategory c m o, Morphism m o) => FiniteCategory (Op c) (OpMorphism m) o Source #
Instance details Defined in Math.Categories.Opposite Methods ob :: Op c -> Set o Source #
type Rep (Op c) Source #
Instance details Defined in Math.Categories.Opposite type Rep (Op c) = D1 ('MetaData "Op" "Math.Categories.Opposite" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "Op" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 c)))

opOp :: Op c -> c Source #

Return the original category given an Op category.