Control.Category

Documentation

class Category cat where

A class for categories. id and (.) must form a monoid.

Methods

id :: cat a a

the identity morphism

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

morphism composition

Instances

Category * (->)

Methods

id :: a -> a

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

Monad m => Category * (Kleisli m)

Methods

id :: Kleisli m a a

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

Category k (Coercion k)

Methods

id :: Coercion k a a

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

Category k ((:~:) k)

Methods

id :: (k :~: a) a

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