Copyright	(c) Erich Gut
License	BSD3
Maintainer	zerich.gut@gmail.com
Safe Haskell	None
Language	Haskell2010

OAlg.Limes.Cone.Duality

Contents

Map
- Covariant
- Contravariant
Orphan instances

Description

definition of duality for Cones over Diagrammatic objects.

Synopsis

cnMapS :: forall s h (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') (p :: Perspective) x y. (HomD s h, NaturalDiagrammatic h d t n m, NaturalDiagrammatic h d (Dual t) n m, p ~ Dual (Dual p)) => h x y -> SDualBi (Cone s p d t n m) x -> SDualBi (Cone s p d t n m) y
cnMapCov :: forall s (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomD s h, NaturalDiagrammatic h d t n m) => Variant2 'Covariant h x y -> Cone s p d t n m x -> Cone s p d t n m y
cnMapMltCov :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomMultiplicativeDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Covariant h x y -> Cone Mlt p d t n m x -> Cone Mlt p d t n m y
cnMapDstCov :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomDistributiveDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Covariant h x y -> Cone Dst p d t n m x -> Cone Dst p d t n m y
cnMap :: forall s h (t :: DiagramType) x y (p :: Perspective) (n :: N') (m :: N'). (Hom s h, t ~ Dual (Dual t)) => h x y -> Cone s p Diagram t n m x -> Cone s p Diagram t n m y
cnMapMlt :: forall h (t :: DiagramType) x y (p :: Perspective) (n :: N') (m :: N'). (HomMultiplicative h, t ~ Dual (Dual t)) => h x y -> Cone Mlt p Diagram t n m x -> Cone Mlt p Diagram t n m y
cnMapDst :: forall h (t :: DiagramType) x y (p :: Perspective) (n :: N') (m :: N'). (HomDistributive h, t ~ Dual (Dual t)) => h x y -> Cone Dst p Diagram t n m x -> Cone Dst p Diagram t n m y
cnMapCnt :: forall s (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomD s h, NaturalDiagrammatic h d t n m) => Variant2 'Contravariant h x y -> Cone s p d t n m x -> Dual1 (Cone s p d t n m) y
cnMapMltCnt :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomMultiplicativeDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Contravariant h x y -> Cone Mlt p d t n m x -> Dual1 (Cone Mlt p d t n m) y
cnMapDstCnt :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomDistributiveDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Contravariant h x y -> Cone Dst p d t n m x -> Dual1 (Cone Dst p d t n m) y

Map

cnMapS :: forall s h (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') (p :: Perspective) x y. (HomD s h, NaturalDiagrammatic h d t n m, NaturalDiagrammatic h d (Dual t) n m, p ~ Dual (Dual p)) => h x y -> SDualBi (Cone s p d t n m) x -> SDualBi (Cone s p d t n m) y Source #

mapping of Cone.

Covariant

cnMapCov :: forall s (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomD s h, NaturalDiagrammatic h d t n m) => Variant2 'Covariant h x y -> Cone s p d t n m x -> Cone s p d t n m y Source #

covariant mapping of Cone.

cnMapMltCov :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomMultiplicativeDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Covariant h x y -> Cone Mlt p d t n m x -> Cone Mlt p d t n m y Source #

mapping of a cone under a Multiplicative covariant homomorphism.

cnMapDstCov :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomDistributiveDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Covariant h x y -> Cone Dst p d t n m x -> Cone Dst p d t n m y Source #

mapping of a cone under a Distributive covariant homomorphism.

cnMap :: forall s h (t :: DiagramType) x y (p :: Perspective) (n :: N') (m :: N'). (Hom s h, t ~ Dual (Dual t)) => h x y -> Cone s p Diagram t n m x -> Cone s p Diagram t n m y Source #

mapping of a cone under a s homomorphism.

cnMapMlt :: forall h (t :: DiagramType) x y (p :: Perspective) (n :: N') (m :: N'). (HomMultiplicative h, t ~ Dual (Dual t)) => h x y -> Cone Mlt p Diagram t n m x -> Cone Mlt p Diagram t n m y Source #

mapping of a cone under a Multiplicative homomorphism.

cnMapDst :: forall h (t :: DiagramType) x y (p :: Perspective) (n :: N') (m :: N'). (HomDistributive h, t ~ Dual (Dual t)) => h x y -> Cone Dst p Diagram t n m x -> Cone Dst p Diagram t n m y Source #

mapping of a cone under a Distributive homomorphism.

Contravariant

cnMapCnt :: forall s (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomD s h, NaturalDiagrammatic h d t n m) => Variant2 'Contravariant h x y -> Cone s p d t n m x -> Dual1 (Cone s p d t n m) y Source #

mapping of a cone under a contravariant homomorphism.

cnMapMltCnt :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomMultiplicativeDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Contravariant h x y -> Cone Mlt p d t n m x -> Dual1 (Cone Mlt p d t n m) y Source #

mapping of a cone under a Multiplicative contravariant homomorphism.

cnMapDstCnt :: forall (h :: Type -> Type -> Type) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x y (p :: Perspective). (HomDistributiveDisjunctive h, NaturalDiagrammatic h d t n m) => Variant2 'Contravariant h x y -> Cone Dst p d t n m x -> Dual1 (Cone Dst p d t n m) y Source #

mapping of a cone under a Distributive contravariant homomorphism.

Orphan instances

(Eq x, EqPoint x) => EqDual1 (Cone s p Diagram t n m :: Type -> Type) (x :: Type) Source #
Instance details
(Show x, ShowPoint x) => ShowDual1 (Cone s p Diagram t n m :: Type -> Type) (x :: Type) Source #
Instance details
(HomDistributiveDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (Cone Dst p d t n m)) h (->) Source #
Instance details Methods amapG :: h x y -> SDualBi (Cone Dst p d t n m) x -> SDualBi (Cone Dst p d t n m) y Source #
(HomMultiplicativeDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (Cone Mlt p d t n m)) h (->) Source #
Instance details Methods amapG :: h x y -> SDualBi (Cone Mlt p d t n m) x -> SDualBi (Cone Mlt p d t n m) y Source #
(HomDistributiveDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => FunctorialG (SDualBi (Cone Dst p d t n m)) h (->) Source #
Instance details
(HomMultiplicativeDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => FunctorialG (SDualBi (Cone Mlt p d t n m)) h (->) Source #
Instance details