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

OAlg.Limes.Cone.Conic.Duality

Contents

Duality
Map
Orphan instances

Description

duality for conic objects.

Synopsis

type NaturalConicBi (h :: Type -> Type -> Type) (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') = (NaturalConic h c s p d t n m, NaturalConic h c s (Dual p) d (Dual t) n m)
sdbToCncObj :: forall (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. Dual1 (c s p d t n m) ~ c s (Dual p) d (Dual t) n m => SDualBi (ConeG c s p d t n m) x -> SDualBi (c s p d t n m) x
sdbFromCncObj :: forall (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. Dual1 (c s p d t n m) ~ c s (Dual p) d (Dual t) n m => SDualBi (c s p d t n m) x -> SDualBi (ConeG c s p d t n m) x

Duality

type NaturalConicBi (h :: Type -> Type -> Type) (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') = (NaturalConic h c s p d t n m, NaturalConic h c s (Dual p) d (Dual t) n m) Source #

natrual conic for p, t and also Dual p, Dual t.

Map

sdbToCncObj :: forall (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. Dual1 (c s p d t n m) ~ c s (Dual p) d (Dual t) n m => SDualBi (ConeG c s p d t n m) x -> SDualBi (c s p d t n m) x Source #

canonical mapping to its underlying conic object.

sdbFromCncObj :: forall (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. Dual1 (c s p d t n m) ~ c s (Dual p) d (Dual t) n m => SDualBi (c s p d t n m) x -> SDualBi (ConeG c s p d t n m) x Source #

canonical mapping from its underlying conic object.

Orphan instances

(HomDistributiveDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => NaturalConic h Cone Dst p d t n m Source #
Instance details
(HomMultiplicativeDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => NaturalConic h Cone Mlt p d t n m Source #
Instance details
(HomDistributiveDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => NaturalTransformable h (->) (SDualBi (ConeG Cone Dst p d t n m)) (SDualBi (ConeG Cone Dst p d t n m)) Source #
Instance details
(HomMultiplicativeDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => NaturalTransformable h (->) (SDualBi (ConeG Cone Mlt p d t n m)) (SDualBi (ConeG Cone Mlt p d t n m)) Source #
Instance details
(HomDistributiveDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConeG Cone Dst p d t n m)) h (->) Source #
Instance details Methods amapG :: h x y -> SDualBi (ConeG Cone Dst p d t n m) x -> SDualBi (ConeG Cone Dst p d t n m) y Source #
(HomMultiplicativeDisjunctive h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConeG Cone Mlt p d t n m)) h (->) Source #
Instance details Methods amapG :: h x y -> SDualBi (ConeG Cone Mlt p d t n m) x -> SDualBi (ConeG Cone Mlt p d t n m) y Source #
(HomDistributiveDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p), t ~ Dual (Dual t)) => FunctorialG (SDualBi (ConeG 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), t ~ Dual (Dual t)) => FunctorialG (SDualBi (ConeG Cone Mlt p d t n m)) h (->) Source #
Instance details