Control.Category

Documentation

class Category cat where

A class for categories. Instances should satisfy the laws

Right identity

f . id = f

Left identity

id . f = f

Associativity

f . (g . h) = (f . g) . h

Methods

id :: cat a a

the identity morphism

(.) :: cat b c -> cat a b -> cat a c infixr 9

morphism composition

Instances

Category Op

Defined in Data.Functor.Contravariant

Methods

id :: forall (a :: k). Op a a

(.) :: forall (b :: k) (c :: k) (a :: k). Op b c -> Op a b -> Op a c

Monad m => Category (Kleisli m :: Type -> Type -> TYPE LiftedRep)

Since: base-3.0

Defined in Control.Arrow

Methods

id :: forall (a :: k). Kleisli m a a

(.) :: forall (b :: k) (c :: k) (a :: k). Kleisli m b c -> Kleisli m a b -> Kleisli m a c

Category (Coercion :: k -> k -> Type)

Since: base-4.7.0.0

Defined in Control.Category

Methods

id :: forall (a :: k0). Coercion a a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). Coercion b c -> Coercion a b -> Coercion a c

Category ((:~:) :: k -> k -> Type)

Since: base-4.7.0.0

Defined in Control.Category

Methods

id :: forall (a :: k0). a :~: a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~: c) -> (a :~: b) -> a :~: c

Category (->)

Since: base-3.0

Defined in Control.Category

Methods

id :: forall (a :: k). a -> a

(.) :: forall (b :: k) (c :: k) (a :: k). (b -> c) -> (a -> b) -> a -> c

Category ((:~~:) :: k -> k -> Type)

Since: base-4.10.0.0

Defined in Control.Category

Methods

id :: forall (a :: k0). a :~~: a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~~: c) -> (a :~~: b) -> a :~~: c

(<<<) :: Category cat => cat b c -> cat a b -> cat a c infixr 1

Right-to-left composition

(>>>) :: Category cat => cat a b -> cat b c -> cat a c infixr 1

Left-to-right composition