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

OAlg.Limes.Cone.Conic.Core

Contents

Conic
Natural

Description

basic definition for objects with a naturally underlying cone.

Synopsis

class Conic (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) where
- cone :: forall s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. c s p d t n m x -> Cone s p d t n m x
newtype ConeG (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 = ConeG (c s p d t n m x)
class (Conic c, HomMultiplicativeDisjunctive h, FunctorialOriented h, NaturalDiagrammatic h d t n m, NaturalTransformable h (->) (SDualBi (ConeG c s p d t n m)) (SDualBi (ConeG Cone s p d t n m)), p ~ Dual (Dual p)) => NaturalConic (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')
crohS :: 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. Conic c => SDualBi (ConeG c s p d t n m) x -> SDualBi (ConeG Cone s p d t n m) x

Conic

class Conic (c :: Type -> Perspective -> (DiagramType -> N' -> N' -> Type -> Type) -> DiagramType -> N' -> N' -> Type -> Type) where Source #

object c having an underlying Cone.

Methods

cone :: forall s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. c s p d t n m x -> Cone s p d t n m x Source #

Instances

Instances details

Conic ConeLiftable Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods cone :: forall s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. ConeLiftable s p d t n m x -> Cone s p d t n m x Source #
Conic Cone Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Core Methods cone :: forall s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. Cone s p d t n m x -> Cone s p d t n m x Source #
Conic ConeZeroHead Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Core Methods cone :: forall s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. ConeZeroHead s p d t n m x -> Cone s p d t n m x Source #
Conic c => Conic (ConicFreeTip c) Source #
Instance details Defined in OAlg.Entity.Slice.Free Methods cone :: forall s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. ConicFreeTip c s p d t n m x -> Cone s p d t n m x Source #
Conic (LiftableCone i) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable Methods cone :: forall s (p :: Perspective) (d :: DiagramType -> N' -> N' -> Type -> Type) (t :: DiagramType) (n :: N') (m :: N') x. LiftableCone i s p d t n m x -> Cone s p d t n m x Source #

newtype ConeG (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 Source #

wrapper for Conic-objects.

Constructors

ConeG (c s p d t n m x)

Instances

Instances details

Conic c => Natural r (->) (SDualBi (ConeG c s p d t n m)) (SDualBi (ConeG Cone s p d t n m)) Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Core Methods roh :: Struct r x -> SDualBi (ConeG c s p d t n m) x -> SDualBi (ConeG Cone s p d t n m) x Source #
(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 Defined in OAlg.Limes.Cone.Conic.Duality
(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 Defined in OAlg.Limes.Cone.Conic.Duality
(HomDistributiveDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => NaturalTransformable h (->) (SDualBi (ConeG ConeZeroHead Mlt p d t n m)) (SDualBi (ConeG Cone Mlt p d t n m)) Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Duality
Conic c => Natural r (->) (ConeG c s p d t n m) (ConeG Cone s p d t n m) Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Core Methods roh :: Struct r x -> ConeG c s p d t n m x -> ConeG Cone s p d t n m x Source #
(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 Defined in OAlg.Limes.Cone.Conic.Duality 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 Defined in OAlg.Limes.Cone.Conic.Duality 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, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => ApplicativeG (SDualBi (ConeG ConeZeroHead s p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Duality Methods amapG :: h x y -> SDualBi (ConeG ConeZeroHead s p d t n m) x -> SDualBi (ConeG ConeZeroHead s 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 Defined in OAlg.Limes.Cone.Conic.Duality
(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 Defined in OAlg.Limes.Cone.Conic.Duality
(HomDistributiveDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => FunctorialG (SDualBi (ConeG ConeZeroHead s p d t n m)) h (->) Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Duality
(CategoryDisjunctive h, HomSlicedDistributive i h, FunctorialOriented h, p ~ Dual (Dual p), t ~ Dual (Dual t)) => ApplicativeG (SDualBi (ConeG (LiftableCone i) s p d t n m)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable Methods amapG :: Inv2 h x y -> SDualBi (ConeG (LiftableCone i) s p d t n m) x -> SDualBi (ConeG (LiftableCone i) s p d t n m) y Source #
(CategoryDisjunctive h, HomSlicedDistributive i h, FunctorialOriented h, p ~ Dual (Dual p), t ~ Dual (Dual t)) => FunctorialG (SDualBi (ConeG (LiftableCone i) s p d t n m)) (Inv2 h) (->) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable
(CategoryDisjunctive h, HomSlicedDistributive i h, FunctorialOriented h, p ~ Dual (Dual p), t ~ Dual (Dual t), s ~ Dst) => NaturalTransformable (Inv2 h) (->) (SDualBi (ConeG (LiftableCone i) s p Diagram t n m)) (SDualBi (ConeG Cone s p Diagram t n m)) Source #
Instance details Defined in OAlg.Entity.Slice.Liftable
Show (c s p d t n m x) => Show (ConeG c s p d t n m x) Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Core Methods showsPrec :: Int -> ConeG c s p d t n m x -> ShowS # show :: ConeG c s p d t n m x -> String # showList :: [ConeG c s p d t n m x] -> ShowS #
Eq (c s p d t n m x) => Eq (ConeG c s p d t n m x) Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Core Methods (==) :: ConeG c s p d t n m x -> ConeG c s p d t n m x -> Bool # (/=) :: ConeG c s p d t n m x -> ConeG c s p d t n m x -> Bool #
type Dual1 (ConeG c s p d t n m :: Type -> Type) Source #
Instance details Defined in OAlg.Limes.Cone.Conic.Core type Dual1 (ConeG c s p d t n m :: Type -> Type) = ConeG c s (Dual p) d (Dual t) n m

Natural

class (Conic c, HomMultiplicativeDisjunctive h, FunctorialOriented h, NaturalDiagrammatic h d t n m, NaturalTransformable h (->) (SDualBi (ConeG c s p d t n m)) (SDualBi (ConeG Cone s p d t n m)), p ~ Dual (Dual p)) => NaturalConic (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') Source #

natural transformation for Conic objects from SDualBi (ConeG c s p d t n m) to SDualBi (Cone s p d t n m).

Instances

Instances details

(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 Defined in OAlg.Limes.Cone.Conic.Duality
(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 Defined in OAlg.Limes.Cone.Conic.Duality
(HomDistributiveDisjunctive h, FunctorialOriented h, NaturalDiagrammaticBi h d t n m, p ~ Dual (Dual p)) => NaturalConic h ConeZeroHead Mlt p d t n m Source #
Instance details Defined in OAlg.Limes.Cone.ZeroHead.Duality
(CategoryDisjunctive h, HomSlicedDistributive i h, FunctorialOriented h, p ~ Dual (Dual p), t ~ Dual (Dual t), s ~ Dst) => NaturalConic (Inv2 h) (LiftableCone i) s p Diagram t n m Source #
Instance details Defined in OAlg.Entity.Slice.Liftable

crohS :: 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. Conic c => SDualBi (ConeG c s p d t n m) x -> SDualBi (ConeG Cone s p d t n m) x Source #

natural assocition induced by croh betewwn SDualBi (ConeG c s p d t n m) and SDualBi (Cone s p d t n m).