Copyright	Guillaume Sabbagh 2022
License	GPL-3
Maintainer	guillaumesabbagh@protonmail.com
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Math.FiniteCategories.Square

Description

The Square category contains 4 generating arrows forming a square. It has 6 non identity arrows.

Synopsis

data SquareOb
- = SquareA
- | SquareB
- | SquareC
- | SquareD
data SquareAr
- = SquareIdA
- | SquareIdB
- | SquareIdC
- | SquareIdD
- | SquareF
- | SquareG
- | SquareH
- | SquareI
- | SquareFH
- | SquareGI
data Square = Square

Documentation

data SquareOb Source #

Objects of the Square category.

Constructors

SquareA
SquareB
SquareC
SquareD

Instances

Instances details

PrettyPrint SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods pprint :: Int -> SquareOb -> String Source # pprintWithIndentations :: Int -> Int -> String -> SquareOb -> String Source # pprintIndent :: Int -> SquareOb -> String Source #
Simplifiable SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods simplify :: SquareOb -> SquareOb #
Generic SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Associated Types type Rep SquareOb :: Type -> Type # Methods from :: SquareOb -> Rep SquareOb x # to :: Rep SquareOb x -> SquareOb #
Show SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods showsPrec :: Int -> SquareOb -> ShowS # show :: SquareOb -> String # showList :: [SquareOb] -> ShowS #
Eq SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods (==) :: SquareOb -> SquareOb -> Bool # (/=) :: SquareOb -> SquareOb -> Bool #
Morphism SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods (@) :: SquareAr -> SquareAr -> SquareAr Source # (@?) :: SquareAr -> SquareAr -> Maybe SquareAr Source # source :: SquareAr -> SquareOb Source # target :: SquareAr -> SquareOb Source #
Category Square SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods identity :: Square -> SquareOb -> SquareAr Source # ar :: Square -> SquareOb -> SquareOb -> Set SquareAr Source # genAr :: Square -> SquareOb -> SquareOb -> Set SquareAr Source # decompose :: Square -> SquareAr -> [SquareAr] Source #
FiniteCategory Square SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods ob :: Square -> Set SquareOb Source #
type Rep SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square type Rep SquareOb = D1 ('MetaData "SquareOb" "Math.FiniteCategories.Square" "FiniteCategories-0.6.0.1-L2v014CZIYe4CTCeXkyH5k" 'False) ((C1 ('MetaCons "SquareA" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "SquareB" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "SquareC" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "SquareD" 'PrefixI 'False) (U1 :: Type -> Type)))

data SquareAr Source #

Morphisms of the Square category.

Constructors

SquareIdA
SquareIdB
SquareIdC
SquareIdD
SquareF
SquareG
SquareH
SquareI
SquareFH
SquareGI

Instances

Instances details

PrettyPrint SquareAr Source #
Instance details Defined in Math.FiniteCategories.Square Methods pprint :: Int -> SquareAr -> String Source # pprintWithIndentations :: Int -> Int -> String -> SquareAr -> String Source # pprintIndent :: Int -> SquareAr -> String Source #
Simplifiable SquareAr Source #
Instance details Defined in Math.FiniteCategories.Square Methods simplify :: SquareAr -> SquareAr #
Generic SquareAr Source #
Instance details Defined in Math.FiniteCategories.Square Associated Types type Rep SquareAr :: Type -> Type # Methods from :: SquareAr -> Rep SquareAr x # to :: Rep SquareAr x -> SquareAr #
Show SquareAr Source #
Instance details Defined in Math.FiniteCategories.Square Methods showsPrec :: Int -> SquareAr -> ShowS # show :: SquareAr -> String # showList :: [SquareAr] -> ShowS #
Eq SquareAr Source #
Instance details Defined in Math.FiniteCategories.Square Methods (==) :: SquareAr -> SquareAr -> Bool # (/=) :: SquareAr -> SquareAr -> Bool #
Morphism SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods (@) :: SquareAr -> SquareAr -> SquareAr Source # (@?) :: SquareAr -> SquareAr -> Maybe SquareAr Source # source :: SquareAr -> SquareOb Source # target :: SquareAr -> SquareOb Source #
Category Square SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods identity :: Square -> SquareOb -> SquareAr Source # ar :: Square -> SquareOb -> SquareOb -> Set SquareAr Source # genAr :: Square -> SquareOb -> SquareOb -> Set SquareAr Source # decompose :: Square -> SquareAr -> [SquareAr] Source #
FiniteCategory Square SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods ob :: Square -> Set SquareOb Source #
type Rep SquareAr Source #
Instance details Defined in Math.FiniteCategories.Square type Rep SquareAr = D1 ('MetaData "SquareAr" "Math.FiniteCategories.Square" "FiniteCategories-0.6.0.1-L2v014CZIYe4CTCeXkyH5k" 'False) (((C1 ('MetaCons "SquareIdA" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "SquareIdB" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "SquareIdC" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "SquareIdD" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "SquareF" 'PrefixI 'False) (U1 :: Type -> Type)))) :+: ((C1 ('MetaCons "SquareG" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "SquareH" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "SquareI" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "SquareFH" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "SquareGI" 'PrefixI 'False) (U1 :: Type -> Type)))))

data Square Source #

The Square category.

Constructors

Square

Instances

Instances details

PrettyPrint Square Source #
Instance details Defined in Math.FiniteCategories.Square Methods pprint :: Int -> Square -> String Source # pprintWithIndentations :: Int -> Int -> String -> Square -> String Source # pprintIndent :: Int -> Square -> String Source #
Simplifiable Square Source #
Instance details Defined in Math.FiniteCategories.Square Methods simplify :: Square -> Square #
Generic Square Source #
Instance details Defined in Math.FiniteCategories.Square Associated Types type Rep Square :: Type -> Type # Methods from :: Square -> Rep Square x # to :: Rep Square x -> Square #
Show Square Source #
Instance details Defined in Math.FiniteCategories.Square Methods showsPrec :: Int -> Square -> ShowS # show :: Square -> String # showList :: [Square] -> ShowS #
Eq Square Source #
Instance details Defined in Math.FiniteCategories.Square Methods (==) :: Square -> Square -> Bool # (/=) :: Square -> Square -> Bool #
Category Square SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods identity :: Square -> SquareOb -> SquareAr Source # ar :: Square -> SquareOb -> SquareOb -> Set SquareAr Source # genAr :: Square -> SquareOb -> SquareOb -> Set SquareAr Source # decompose :: Square -> SquareAr -> [SquareAr] Source #
FiniteCategory Square SquareAr SquareOb Source #
Instance details Defined in Math.FiniteCategories.Square Methods ob :: Square -> Set SquareOb Source #
type Rep Square Source #
Instance details Defined in Math.FiniteCategories.Square type Rep Square = D1 ('MetaData "Square" "Math.FiniteCategories.Square" "FiniteCategories-0.6.0.1-L2v014CZIYe4CTCeXkyH5k" 'False) (C1 ('MetaCons "Square" 'PrefixI 'False) (U1 :: Type -> Type))