Control.Category

Documentation

class Category cat where

A class for categories. Instances should satisfy the laws

f . id  =  f  -- (right identity)
id . f  =  f  -- (left identity)
f . (g . h)  =  (f . g) . h  -- (associativity)

Minimal complete definition

id, (.)

Methods

id :: cat a a

the identity morphism

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

morphism composition

Instances

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

Since: 4.7.0.0

Methods

id :: Coercion a a

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

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

Since: 4.7.0.0

Methods

id :: a :~: a

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

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

Since: 4.10.0.0

Methods

id :: a :~~: a

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

Monad m => Category (Kleisli m :: * -> * -> *)

Since: 3.0

Methods

id :: Kleisli m a a

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

Category ((->) :: * -> * -> *)

Since: 3.0

Methods

id :: a -> a

(.) :: (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