Algebra.Category.NatTrans

Documentation

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

Constructors

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

Instances

Category NatTrans

Defined in Algebra.Category.NatTrans

Associated Types

type Obj NatTrans :: k -> Constraint

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

id :: forall (a :: k). Obj NatTrans a => NatTrans a a

Monoidal ((⊗) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (One :: Type -> Type) NatTrans

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)

assoc :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans ((a ⊗ b) ⊗ c) (a ⊗ (b ⊗ c))

assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans (a ⊗ (b ⊗ c)) ((a ⊗ b) ⊗ c)

unitorR :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans a (a ⊗ One)

unitorR_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans (a ⊗ One) a

unitorL :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans a (One ⊗ a)

unitorL_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans One) => NatTrans (One ⊗ a) a

Monoidal ((∘) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Id NatTrans

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)

assoc :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans ((a ∘ b) ∘ c) (a ∘ (b ∘ c))

assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj NatTrans a, Obj NatTrans b, Obj NatTrans c) => NatTrans (a ∘ (b ∘ c)) ((a ∘ b) ∘ c)

unitorR :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans a (a ∘ Id)

unitorR_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans (a ∘ Id) a

unitorL :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans a (Id ∘ a)

unitorL_ :: forall (a :: k). (Obj NatTrans a, Obj NatTrans Id) => NatTrans (Id ∘ a) a

type Obj NatTrans

Defined in Algebra.Category.NatTrans

type Obj NatTrans = Functor