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/Haskell 8

Control.Category

Copyright (c) Ashley Yakeley 2007
License BSD-style (see the LICENSE file in the distribution)
Maintainer [email protected]
Stability experimental
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

class Category cat where Source

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 a Source

the identity morphism

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

morphism composition

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

Since: base-4.7.0.0
Instance details

Defined in Control.Category

Methods

id :: Coercion a a Source

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

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

Since: base-4.7.0.0
Instance details

Defined in Control.Category

Methods

id :: a :~: a Source

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

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

Since: base-4.10.0.0
Instance details

Defined in Control.Category

Methods

id :: a :~~: a Source

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

Category Op
Instance details

Defined in Data.Functor.Contravariant

Methods

id :: Op a a Source

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

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

Since: base-3.0
Instance details

Defined in Control.Arrow

Methods

id :: Kleisli m a a Source

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

Category ((->) :: Type -> Type -> Type)

Since: base-3.0
Instance details

Defined in Control.Category

Methods

id :: a -> a Source

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

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.6.1/docs/html/libraries/base-4.12.0.0/Control-Category.html