base-4.18.1.0: Basic libraries

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