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

Math.FiniteCategories.V

Description

The V category contains two arrows pointing to the same object.

The shape of the V category is the following : B -F-> A <-G- C

Synopsis

data VOb
- = VA
- | VB
- | VC
data VAr
- = VIdA
- | VIdB
- | VIdC
- | VF
- | VG
data V = V

Documentation

data VOb Source #

Objects of the V category.

Constructors

VA
VB
VC

Instances

Instances details

PrettyPrint VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods pprint :: Int -> VOb -> String Source # pprintWithIndentations :: Int -> Int -> String -> VOb -> String Source # pprintIndent :: Int -> VOb -> String Source #
Simplifiable VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods simplify :: VOb -> VOb #
Generic VOb Source #
Instance details Defined in Math.FiniteCategories.V Associated Types type Rep VOb :: Type -> Type Methods from :: VOb -> Rep VOb x to :: Rep VOb x -> VOb
Show VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods showsPrec :: Int -> VOb -> ShowS show :: VOb -> String showList :: [VOb] -> ShowS
Eq VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods (==) :: VOb -> VOb -> Bool (/=) :: VOb -> VOb -> Bool
Morphism VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods (@) :: VAr -> VAr -> VAr Source # (@?) :: VAr -> VAr -> Maybe VAr Source # source :: VAr -> VOb Source # target :: VAr -> VOb Source #
Category V VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods identity :: V -> VOb -> VAr Source # ar :: V -> VOb -> VOb -> Set VAr Source # genAr :: V -> VOb -> VOb -> Set VAr Source # decompose :: V -> VAr -> [VAr] Source #
FiniteCategory V VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods ob :: V -> Set VOb Source #
type Rep VOb Source #
Instance details Defined in Math.FiniteCategories.V type Rep VOb = D1 ('MetaData "VOb" "Math.FiniteCategories.V" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "VA" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "VB" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "VC" 'PrefixI 'False) (U1 :: Type -> Type)))

data VAr Source #

Morphisms of the V category.

Constructors

VIdA
VIdB
VIdC
VF
VG

Instances

Instances details

PrettyPrint VAr Source #
Instance details Defined in Math.FiniteCategories.V Methods pprint :: Int -> VAr -> String Source # pprintWithIndentations :: Int -> Int -> String -> VAr -> String Source # pprintIndent :: Int -> VAr -> String Source #
Simplifiable VAr Source #
Instance details Defined in Math.FiniteCategories.V Methods simplify :: VAr -> VAr #
Generic VAr Source #
Instance details Defined in Math.FiniteCategories.V Associated Types type Rep VAr :: Type -> Type Methods from :: VAr -> Rep VAr x to :: Rep VAr x -> VAr
Show VAr Source #
Instance details Defined in Math.FiniteCategories.V Methods showsPrec :: Int -> VAr -> ShowS show :: VAr -> String showList :: [VAr] -> ShowS
Eq VAr Source #
Instance details Defined in Math.FiniteCategories.V Methods (==) :: VAr -> VAr -> Bool (/=) :: VAr -> VAr -> Bool
Morphism VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods (@) :: VAr -> VAr -> VAr Source # (@?) :: VAr -> VAr -> Maybe VAr Source # source :: VAr -> VOb Source # target :: VAr -> VOb Source #
Category V VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods identity :: V -> VOb -> VAr Source # ar :: V -> VOb -> VOb -> Set VAr Source # genAr :: V -> VOb -> VOb -> Set VAr Source # decompose :: V -> VAr -> [VAr] Source #
FiniteCategory V VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods ob :: V -> Set VOb Source #
type Rep VAr Source #
Instance details Defined in Math.FiniteCategories.V type Rep VAr = D1 ('MetaData "VAr" "Math.FiniteCategories.V" "FiniteCategories-0.6.4.0-inplace" 'False) ((C1 ('MetaCons "VIdA" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "VIdB" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "VIdC" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "VF" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "VG" 'PrefixI 'False) (U1 :: Type -> Type))))

data V Source #

The V category.

Constructors

V

Instances

Instances details

PrettyPrint V Source #
Instance details Defined in Math.FiniteCategories.V Methods pprint :: Int -> V -> String Source # pprintWithIndentations :: Int -> Int -> String -> V -> String Source # pprintIndent :: Int -> V -> String Source #
Simplifiable V Source #
Instance details Defined in Math.FiniteCategories.V Methods simplify :: V -> V #
Generic V Source #
Instance details Defined in Math.FiniteCategories.V Associated Types type Rep V :: Type -> Type Methods from :: V -> Rep V x to :: Rep V x -> V
Show V Source #
Instance details Defined in Math.FiniteCategories.V Methods showsPrec :: Int -> V -> ShowS show :: V -> String showList :: [V] -> ShowS
Eq V Source #
Instance details Defined in Math.FiniteCategories.V Methods (==) :: V -> V -> Bool (/=) :: V -> V -> Bool
Category V VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods identity :: V -> VOb -> VAr Source # ar :: V -> VOb -> VOb -> Set VAr Source # genAr :: V -> VOb -> VOb -> Set VAr Source # decompose :: V -> VAr -> [VAr] Source #
FiniteCategory V VAr VOb Source #
Instance details Defined in Math.FiniteCategories.V Methods ob :: V -> Set VOb Source #
type Rep V Source #
Instance details Defined in Math.FiniteCategories.V type Rep V = D1 ('MetaData "V" "Math.FiniteCategories.V" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "V" 'PrefixI 'False) (U1 :: Type -> Type))