Module Control.Category

Introduction of the type class for categories.

Imports

• import Prelude.PreludeBase as PreludeBase
• import Control.Semigroupoid as Semigroupoid

Table of Content

• Definitions

  class Semigroupoid f ⇒ Category f

• Instances

  instance Category ->

• Functions and Values by Type

Definitions

class Semigroupoid f ⇒ Category f

A category is a Semigroupoid with the following additional properties:

• For every object A, there exists a mophism id(A): A -> A called the identity morphism for A, such that for every morphism f: A -> B we have

 id(B) • f = f = f • id(A)

Known Instances

->

Member Functions

id ∷ Category f ⇒ f a a

the identity morphism

Instances

instance Category ->

The category of Frege functions

Member Functions

id ∷ 𝖆 → 𝖆

Identity on values

id x is x

Functions and Values by Type

𝖆 → 𝖆

Category_->.id

Category f ⇒ f a a

Category.id