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Control.Category

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

Description

class Category cat where Source

A class for categories. Instances should satisfy the laws

Right identity
f . id = f
Left identity
id . f = f
Associativity
f . (g . h) = (f . g) . h

Methods

id :: cat a a Source

the identity morphism

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

morphism composition

Instances
Instances details
Category Op Source
Instance details

Defined in Data.Functor.Contravariant

Methods

id :: forall (a :: k). Op a a Source

(.) :: forall (b :: k) (c :: k) (a :: k). Op b c -> Op a b -> Op a c Source
Monad m => Category (Kleisli m :: Type -> Type -> Type) Source

Since: base-3.0
Instance details

Defined in Control.Arrow

Methods

id :: forall (a :: k). Kleisli m a a Source

(.) :: forall (b :: k) (c :: k) (a :: k). Kleisli m b c -> Kleisli m a b -> Kleisli m a c Source
Category (Coercion :: k -> k -> Type) Source

Since: base-4.7.0.0
Instance details

Defined in Control.Category

Methods

id :: forall (a :: k0). Coercion a a Source

(.) :: forall (b :: k0) (c :: k0) (a :: k0). Coercion b c -> Coercion a b -> Coercion a c Source
Category ((:~:) :: k -> k -> Type) Source

Since: base-4.7.0.0
Instance details

Defined in Control.Category

Methods

id :: forall (a :: k0). a :~: a Source

(.) :: forall (b :: k0) (c :: k0) (a :: k0). (b :~: c) -> (a :~: b) -> a :~: c Source
Category (->) Source

Since: base-3.0
Instance details

Defined in Control.Category

Methods

id :: forall (a :: k). a -> a Source

(.) :: forall (b :: k) (c :: k) (a :: k). (b -> c) -> (a -> b) -> a -> c Source
Category ((:~~:) :: k -> k -> Type) Source

Since: base-4.10.0.0
Instance details

Defined in Control.Category

Methods

id :: forall (a :: k0). a :~~: a Source

(.) :: forall (b :: k0) (c :: k0) (a :: k0). (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/9.4.2/docs/libraries/base-4.17.0.0/Control-Category.html