Copyright	(c) Ashley Yakeley 2007
License	BSD-style (see the LICENSE file in the distribution)
Maintainer	ashley@semantic.org
Stability	experimental
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Category

Description

Synopsis

Documentation

class Category cat where Source

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

Methods

id :: cat a a Source

the identity morphism

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

morphism composition

Instances

Category * (->) Source
Methods id :: (->) a a Source (.) :: (->) b c -> (->) a b -> (->) a c Source
Monad m => Category * (Kleisli m) Source
Methods id :: Kleisli m a a Source (.) :: Kleisli m b c -> Kleisli m a b -> Kleisli m a c Source
Category k (Coercion k) Source
Methods id :: Coercion k a a Source (.) :: Coercion k b c -> Coercion k a b -> Coercion k a c Source
Category k ((:~:) k) Source
Methods id :: (:~:) k a a Source (.) :: (:~:) k b c -> (:~:) k a b -> (:~:) k a c Source

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

Right-to-left composition

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

Left-to-right composition