Copyright	Guillaume Sabbagh 2021
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

UsualCategories.DiscreteCategory

Description

A discrete category is a category with no morphism other than identities.

Synopsis

data DiscreteObject a = DiscreteObject a
data DiscreteIdentity a = DiscreteIdentity a
data DiscreteCategory a = DiscreteCategory [a]

Documentation

data DiscreteObject a Source #

A discrete object is just an usual object.

Constructors

DiscreteObject a

Instances

Instances details

Eq a => Eq (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods (==) :: DiscreteObject a -> DiscreteObject a -> Bool (/=) :: DiscreteObject a -> DiscreteObject a -> Bool
Show a => Show (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods showsPrec :: Int -> DiscreteObject a -> ShowS show :: DiscreteObject a -> String showList :: [DiscreteObject a] -> ShowS
PrettyPrintable a => PrettyPrintable (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods pprint :: DiscreteObject a -> String Source #
Eq a => Morphism (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods (@) :: DiscreteIdentity a -> DiscreteIdentity a -> DiscreteIdentity a Source # source :: DiscreteIdentity a -> DiscreteObject a Source # target :: DiscreteIdentity a -> DiscreteObject a Source #
Eq a => GeneratedFiniteCategory (DiscreteCategory a) (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods genAr :: DiscreteCategory a -> DiscreteObject a -> DiscreteObject a -> [DiscreteIdentity a] Source # decompose :: DiscreteCategory a -> DiscreteIdentity a -> [DiscreteIdentity a] Source # genArrows :: DiscreteCategory a -> [DiscreteIdentity a] Source #
Eq a => FiniteCategory (DiscreteCategory a) (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods ob :: DiscreteCategory a -> [DiscreteObject a] Source # identity :: DiscreteCategory a -> DiscreteObject a -> DiscreteIdentity a Source # ar :: DiscreteCategory a -> DiscreteObject a -> DiscreteObject a -> [DiscreteIdentity a] Source # arrows :: DiscreteCategory a -> [DiscreteIdentity a] Source #

data DiscreteIdentity a Source #

DiscreteIdentity is the morphism of the discrete category.

Constructors

DiscreteIdentity a

Instances

Instances details

Eq a => Eq (DiscreteIdentity a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods (==) :: DiscreteIdentity a -> DiscreteIdentity a -> Bool (/=) :: DiscreteIdentity a -> DiscreteIdentity a -> Bool
Show a => Show (DiscreteIdentity a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods showsPrec :: Int -> DiscreteIdentity a -> ShowS show :: DiscreteIdentity a -> String showList :: [DiscreteIdentity a] -> ShowS
PrettyPrintable a => PrettyPrintable (DiscreteIdentity a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods pprint :: DiscreteIdentity a -> String Source #
Eq a => Morphism (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods (@) :: DiscreteIdentity a -> DiscreteIdentity a -> DiscreteIdentity a Source # source :: DiscreteIdentity a -> DiscreteObject a Source # target :: DiscreteIdentity a -> DiscreteObject a Source #
Eq a => GeneratedFiniteCategory (DiscreteCategory a) (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods genAr :: DiscreteCategory a -> DiscreteObject a -> DiscreteObject a -> [DiscreteIdentity a] Source # decompose :: DiscreteCategory a -> DiscreteIdentity a -> [DiscreteIdentity a] Source # genArrows :: DiscreteCategory a -> [DiscreteIdentity a] Source #
Eq a => FiniteCategory (DiscreteCategory a) (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods ob :: DiscreteCategory a -> [DiscreteObject a] Source # identity :: DiscreteCategory a -> DiscreteObject a -> DiscreteIdentity a Source # ar :: DiscreteCategory a -> DiscreteObject a -> DiscreteObject a -> [DiscreteIdentity a] Source # arrows :: DiscreteCategory a -> [DiscreteIdentity a] Source #

data DiscreteCategory a Source #

The discrete category is just a list of objects.

Constructors

DiscreteCategory [a]

Instances

Instances details

Eq a => Eq (DiscreteCategory a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods (==) :: DiscreteCategory a -> DiscreteCategory a -> Bool (/=) :: DiscreteCategory a -> DiscreteCategory a -> Bool
Show a => Show (DiscreteCategory a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods showsPrec :: Int -> DiscreteCategory a -> ShowS show :: DiscreteCategory a -> String showList :: [DiscreteCategory a] -> ShowS
PrettyPrintable a => PrettyPrintable (DiscreteCategory a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods pprint :: DiscreteCategory a -> String Source #
Eq a => GeneratedFiniteCategory (DiscreteCategory a) (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods genAr :: DiscreteCategory a -> DiscreteObject a -> DiscreteObject a -> [DiscreteIdentity a] Source # decompose :: DiscreteCategory a -> DiscreteIdentity a -> [DiscreteIdentity a] Source # genArrows :: DiscreteCategory a -> [DiscreteIdentity a] Source #
Eq a => FiniteCategory (DiscreteCategory a) (DiscreteIdentity a) (DiscreteObject a) Source #
Instance details Defined in UsualCategories.DiscreteCategory Methods ob :: DiscreteCategory a -> [DiscreteObject a] Source # identity :: DiscreteCategory a -> DiscreteObject a -> DiscreteIdentity a Source # ar :: DiscreteCategory a -> DiscreteObject a -> DiscreteObject a -> [DiscreteIdentity a] Source # arrows :: DiscreteCategory a -> [DiscreteIdentity a] Source #