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

Control.Category

Description

Synopsis

class Category cat where
- id :: cat a a
- (.) :: cat b c -> cat a b -> cat a c
(<<<) :: Category cat => cat b c -> cat a b -> cat a c
(>>>) :: Category cat => cat a b -> cat b c -> cat a c

Documentation

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