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
PrettyPrint m => PrettyPrint (OpMorphism m) Source # | |
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 # | |
Defined in Math.Categories.Opposite Methods simplify :: OpMorphism m -> OpMorphism m # | |
Generic (OpMorphism m) Source # | |
Defined in Math.Categories.Opposite Associated Types type Rep (OpMorphism m) :: Type -> Type | |
Show m => Show (OpMorphism m) Source # | |
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 # | |
Defined in Math.Categories.Opposite | |
Morphism m o => Morphism (OpMorphism m) o Source # | |
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 # | |
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 # | |
type Rep (OpMorphism m) Source # | |
Defined in Math.Categories.Opposite type Rep (OpMorphism m) = D1 ('MetaData "OpMorphism" "Math.Categories.Opposite" "FiniteCategories-0.6.1.0-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
.
Constructors
Op c |
Instances
PrettyPrint c => PrettyPrint (Op c) Source # | |
Defined in Math.Categories.Opposite | |
Simplifiable c => Simplifiable (Op c) Source # | |
Defined in Math.Categories.Opposite | |
Generic (Op c) Source # | |
Show c => Show (Op c) Source # | |
Eq c => Eq (Op c) Source # | |
(Category c m o, Morphism m o) => Category (Op c) (OpMorphism m) o Source # | |
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 # | |
type Rep (Op c) Source # | |
Defined in Math.Categories.Opposite type Rep (Op c) = D1 ('MetaData "Op" "Math.Categories.Opposite" "FiniteCategories-0.6.1.0-inplace" 'False) (C1 ('MetaCons "Op" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 c))) |