Math.Categories.Opposite

Each Category has an opposite one where morphisms are reversed.

Documentation

data OpMorphism m

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

Constructors

OpMorphism m

Instances

Eq m => Eq (OpMorphism m)

Defined in Math.Categories.Opposite

Methods

(==) :: OpMorphism m -> OpMorphism m -> Bool

(/=) :: OpMorphism m -> OpMorphism m -> Bool

Show m => Show (OpMorphism m)

Defined in Math.Categories.Opposite

Methods

showsPrec :: Int -> OpMorphism m -> ShowS

show :: OpMorphism m -> String

showList :: [OpMorphism m] -> ShowS

PrettyPrint m => PrettyPrint (OpMorphism m)

Defined in Math.Categories.Opposite

Methods

pprint :: OpMorphism m -> String

Morphism m o => Morphism (OpMorphism m) o

Defined in Math.Categories.Opposite

Methods

(@?) :: OpMorphism m -> OpMorphism m -> Maybe (OpMorphism m)

source :: OpMorphism m -> o

target :: OpMorphism m -> o

(Category c m o, Morphism m o) => Category (Op c) (OpMorphism m) o

Defined in Math.Categories.Opposite

Methods

identity :: Op c -> o -> OpMorphism m

ar :: Op c -> o -> o -> Set (OpMorphism m)

genAr :: Op c -> o -> o -> Set (OpMorphism m)

decompose :: Op c -> OpMorphism m -> [OpMorphism m]

(FiniteCategory c m o, Morphism m o) => FiniteCategory (Op c) (OpMorphism m) o

Defined in Math.Categories.Opposite

Methods

ob :: Op c -> Set o

opOpMorphism :: OpMorphism m -> m

Return the original morphism given an OpMorphism.

data Op c

The Op operator gives the opposite of a Category.

Constructors

Op c

Instances

Eq c => Eq (Op c)

Defined in Math.Categories.Opposite

Methods

(==) :: Op c -> Op c -> Bool

(/=) :: Op c -> Op c -> Bool

Show c => Show (Op c)

Defined in Math.Categories.Opposite

Methods

showsPrec :: Int -> Op c -> ShowS

show :: Op c -> String

showList :: [Op c] -> ShowS

PrettyPrint c => PrettyPrint (Op c)

Defined in Math.Categories.Opposite

Methods

pprint :: Op c -> String

(Category c m o, Morphism m o) => Category (Op c) (OpMorphism m) o

Defined in Math.Categories.Opposite

Methods

identity :: Op c -> o -> OpMorphism m

ar :: Op c -> o -> o -> Set (OpMorphism m)

genAr :: Op c -> o -> o -> Set (OpMorphism m)

decompose :: Op c -> OpMorphism m -> [OpMorphism m]

(FiniteCategory c m o, Morphism m o) => FiniteCategory (Op c) (OpMorphism m) o

Defined in Math.Categories.Opposite

Methods

ob :: Op c -> Set o

opOp :: Op c -> c

Return the original category given an Op category.