Safe Haskell	Safe-Inferred
Language	Haskell2010

Algebra.Category.NatTrans

Documentation

newtype NatTrans (f :: Type -> Type) (g :: Type -> Type) Source #

Constructors

NatTrans (forall x. f x -> g x)

Instances

Instances details

Category NatTrans Source #
Instance details Defined in Algebra.Category.NatTrans Associated Types type Obj NatTrans :: k -> Constraint Source # Methods (.) :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans b c -> NatTrans a b -> NatTrans a c Source # id :: forall (a :: k). Obj NatTrans a => NatTrans a a Source #
Monoidal ((⊗) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (One :: Type -> Type) NatTrans Source #
Instance details Defined in Algebra.Category.NatTrans Methods (⊗) :: forall (a :: k) (b :: k) (c :: k) (d :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c, Obj NatTrans d) => NatTrans a b -> NatTrans c d -> NatTrans (a ⊗ c) (b ⊗ d) Source # assoc :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans ((a ⊗ b) ⊗ c) (a ⊗ (b ⊗ c)) Source # assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans (a ⊗ (b ⊗ c)) ((a ⊗ b) ⊗ c) Source # unitorR :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans a (a ⊗ One) Source # unitorR_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans (a ⊗ One) a Source # unitorL :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans a (One ⊗ a) Source # unitorL_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans (One ⊗ a) a Source #
Monoidal ((∘) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Id NatTrans Source #
Instance details Defined in Algebra.Category.NatTrans Methods (⊗) :: forall (a :: k) (b :: k) (c :: k) (d :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c, Obj NatTrans d) => NatTrans a b -> NatTrans c d -> NatTrans (a ∘ c) (b ∘ d) Source # assoc :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans ((a ∘ b) ∘ c) (a ∘ (b ∘ c)) Source # assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans (a ∘ (b ∘ c)) ((a ∘ b) ∘ c) Source # unitorR :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans a (a ∘ Id) Source # unitorR_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans (a ∘ Id) a Source # unitorL :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans a (Id ∘ a) Source # unitorL_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans (Id ∘ a) a Source #
type Obj NatTrans Source #
Instance details Defined in Algebra.Category.NatTrans type Obj NatTrans = Functor