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

UsualCategories.Three

Description

The 3 category contains three object A, B and C and three morphisms F : A -> B, G : B -> C, G*F : A -> C (and of course three identities).

Synopsis

data ThreeOb
- = A
- | B
- | C
data ThreeAr
- = IdA
- | IdB
- | IdC
- | F
- | G
- | GF
data Three = Three

Documentation

data ThreeOb Source #

Object of the 3 category.

Constructors

A
B
C

Instances

Instances details

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

data ThreeAr Source #

Morphism of the 3 category.

Constructors

IdA
IdB
IdC
F
G
GF

Instances

Instances details

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

data Three Source #

The 3 category.

Constructors

Three

Instances

Instances details

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