Math.FiniteCategories.V

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

Documentation

data VOb

Objects of the V category.

Constructors

VA

VB

VC

Instances

PrettyPrint VOb

Defined in Math.FiniteCategories.V

Methods

pprint :: Int -> VOb -> String

pprintWithIndentations :: Int -> Int -> String -> VOb -> String

pprintIndent :: Int -> VOb -> String

Simplifiable VOb

Defined in Math.FiniteCategories.V

Methods

simplify :: VOb -> VOb

Generic VOb

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

Defined in Math.FiniteCategories.V

Methods

showsPrec :: Int -> VOb -> ShowS

show :: VOb -> String

showList :: [VOb] -> ShowS

Eq VOb

Defined in Math.FiniteCategories.V

Methods

(==) :: VOb -> VOb -> Bool

(/=) :: VOb -> VOb -> Bool

Morphism VAr VOb

Defined in Math.FiniteCategories.V

Methods

(@) :: VAr -> VAr -> VAr

(@?) :: VAr -> VAr -> Maybe VAr

source :: VAr -> VOb

target :: VAr -> VOb

Category V VAr VOb

Defined in Math.FiniteCategories.V

Methods

identity :: V -> VOb -> VAr

ar :: V -> VOb -> VOb -> Set VAr

genAr :: V -> VOb -> VOb -> Set VAr

decompose :: V -> VAr -> [VAr]

FiniteCategory V VAr VOb

Defined in Math.FiniteCategories.V

Methods

ob :: V -> Set VOb

type Rep VOb

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

Morphisms of the V category.

Constructors

VIdA

VIdB

VIdC

VF

VG

Instances

PrettyPrint VAr

Defined in Math.FiniteCategories.V

Methods

pprint :: Int -> VAr -> String

pprintWithIndentations :: Int -> Int -> String -> VAr -> String

pprintIndent :: Int -> VAr -> String

Simplifiable VAr

Defined in Math.FiniteCategories.V

Methods

simplify :: VAr -> VAr

Generic VAr

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

Defined in Math.FiniteCategories.V

Methods

showsPrec :: Int -> VAr -> ShowS

show :: VAr -> String

showList :: [VAr] -> ShowS

Eq VAr

Defined in Math.FiniteCategories.V

Methods

(==) :: VAr -> VAr -> Bool

(/=) :: VAr -> VAr -> Bool

Morphism VAr VOb

Defined in Math.FiniteCategories.V

Methods

(@) :: VAr -> VAr -> VAr

(@?) :: VAr -> VAr -> Maybe VAr

source :: VAr -> VOb

target :: VAr -> VOb

Category V VAr VOb

Defined in Math.FiniteCategories.V

Methods

identity :: V -> VOb -> VAr

ar :: V -> VOb -> VOb -> Set VAr

genAr :: V -> VOb -> VOb -> Set VAr

decompose :: V -> VAr -> [VAr]

FiniteCategory V VAr VOb

Defined in Math.FiniteCategories.V

Methods

ob :: V -> Set VOb

type Rep VAr

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

The V category.

Constructors

V

Instances

PrettyPrint V

Defined in Math.FiniteCategories.V

Methods

pprint :: Int -> V -> String

pprintWithIndentations :: Int -> Int -> String -> V -> String

pprintIndent :: Int -> V -> String

Simplifiable V

Defined in Math.FiniteCategories.V

Methods

simplify :: V -> V

Generic V

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

Defined in Math.FiniteCategories.V

Methods

showsPrec :: Int -> V -> ShowS

show :: V -> String

showList :: [V] -> ShowS

Eq V

Defined in Math.FiniteCategories.V

Methods

(==) :: V -> V -> Bool

(/=) :: V -> V -> Bool

Category V VAr VOb

Defined in Math.FiniteCategories.V

Methods

identity :: V -> VOb -> VAr

ar :: V -> VOb -> VOb -> Set VAr

genAr :: V -> VOb -> VOb -> Set VAr

decompose :: V -> VAr -> [VAr]

FiniteCategory V VAr VOb

Defined in Math.FiniteCategories.V

Methods

ob :: V -> Set VOb

type Rep V

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))