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

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)

Methods

id :: cat a aSource #

the identity morphism

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

morphism composition

Instances

Category (Coercion :: k -> k ->Type)Source #	Since: 4.7.0.0
Instance details Defined inControl.Category Methods id ::Coercion a aSource # (.) ::Coercion b c ->Coercion a b ->Coercion a cSource #
Category ((:~:) :: k -> k ->Type)Source #	Since: 4.7.0.0
Instance details Defined inControl.Category Methods id :: a:~: aSource # (.) :: (b:~: c) -> (a:~: b) -> a:~: cSource #
Category ((:~~:) :: k -> k ->Type)Source #	Since: 4.10.0.0
Instance details Defined inControl.Category Methods id :: a:~~: aSource # (.) :: (b:~~: c) -> (a:~~: b) -> a:~~: cSource #
Category OpSource #
Instance details Defined inData.Functor.Contravariant Methods id ::Op a aSource # (.) ::Op b c ->Op a b ->Op a cSource #
Monad m =>Category (Kleisli m ::Type ->Type ->Type)Source #	Since: 3.0
Instance details Defined inControl.Arrow Methods id ::Kleisli m a aSource # (.) ::Kleisli m b c ->Kleisli m a b ->Kleisli m a cSource #
Category ((->) ::Type ->Type ->Type)Source #	Since: 3.0
Instance details Defined inControl.Category Methods id :: a -> aSource # (.) :: (b -> c) -> (a -> b) -> a -> cSource #

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

Right-to-left composition

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

Left-to-right composition

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