Math.FiniteCategories.Hat

The Hat category contains two arrows coming from the same object.

The shape of Hat is the following : B `A` -`G`- C

Documentation

data HatOb

Objects of the Hat category.

Constructors

HatA

HatB

HatC

Instances

PrettyPrint HatOb

Defined in Math.FiniteCategories.Hat

Methods

pprint :: Int -> HatOb -> String

pprintWithIndentations :: Int -> Int -> String -> HatOb -> String

pprintIndent :: Int -> HatOb -> String

Simplifiable HatOb

Defined in Math.FiniteCategories.Hat

Methods

simplify :: HatOb -> HatOb

Generic HatOb

Defined in Math.FiniteCategories.Hat

Associated Types

type Rep HatOb :: Type -> Type

Methods

from :: HatOb -> Rep HatOb x

to :: Rep HatOb x -> HatOb

Show HatOb

Defined in Math.FiniteCategories.Hat

Methods

showsPrec :: Int -> HatOb -> ShowS

show :: HatOb -> String

showList :: [HatOb] -> ShowS

Eq HatOb

Defined in Math.FiniteCategories.Hat

Methods

(==) :: HatOb -> HatOb -> Bool

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

Morphism HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

(@) :: HatAr -> HatAr -> HatAr

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

source :: HatAr -> HatOb

target :: HatAr -> HatOb

Category Hat HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

identity :: Hat -> HatOb -> HatAr

ar :: Hat -> HatOb -> HatOb -> Set HatAr

genAr :: Hat -> HatOb -> HatOb -> Set HatAr

decompose :: Hat -> HatAr -> [HatAr]

FiniteCategory Hat HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

ob :: Hat -> Set HatOb

type Rep HatOb

Defined in Math.FiniteCategories.Hat

type Rep HatOb = D1 ('MetaData "HatOb" "Math.FiniteCategories.Hat" "FiniteCategories-0.6.0.1-L2v014CZIYe4CTCeXkyH5k" 'False) (C1 ('MetaCons "HatA" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "HatB" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "HatC" 'PrefixI 'False) (U1 :: Type -> Type)))

data HatAr

Morphisms of the Hat category.

Constructors

HatIdA

HatIdB

HatIdC

HatF

HatG

Instances

PrettyPrint HatAr

Defined in Math.FiniteCategories.Hat

Methods

pprint :: Int -> HatAr -> String

pprintWithIndentations :: Int -> Int -> String -> HatAr -> String

pprintIndent :: Int -> HatAr -> String

Simplifiable HatAr

Defined in Math.FiniteCategories.Hat

Methods

simplify :: HatAr -> HatAr

Generic HatAr

Defined in Math.FiniteCategories.Hat

Associated Types

type Rep HatAr :: Type -> Type

Methods

from :: HatAr -> Rep HatAr x

to :: Rep HatAr x -> HatAr

Show HatAr

Defined in Math.FiniteCategories.Hat

Methods

showsPrec :: Int -> HatAr -> ShowS

show :: HatAr -> String

showList :: [HatAr] -> ShowS

Eq HatAr

Defined in Math.FiniteCategories.Hat

Methods

(==) :: HatAr -> HatAr -> Bool

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

Morphism HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

(@) :: HatAr -> HatAr -> HatAr

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

source :: HatAr -> HatOb

target :: HatAr -> HatOb

Category Hat HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

identity :: Hat -> HatOb -> HatAr

ar :: Hat -> HatOb -> HatOb -> Set HatAr

genAr :: Hat -> HatOb -> HatOb -> Set HatAr

decompose :: Hat -> HatAr -> [HatAr]

FiniteCategory Hat HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

ob :: Hat -> Set HatOb

type Rep HatAr

Defined in Math.FiniteCategories.Hat

type Rep HatAr = D1 ('MetaData "HatAr" "Math.FiniteCategories.Hat" "FiniteCategories-0.6.0.1-L2v014CZIYe4CTCeXkyH5k" 'False) ((C1 ('MetaCons "HatIdA" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "HatIdB" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "HatIdC" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "HatF" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "HatG" 'PrefixI 'False) (U1 :: Type -> Type))))

data Hat

The Hat category.

Constructors

Hat

Instances

PrettyPrint Hat

Defined in Math.FiniteCategories.Hat

Methods

pprint :: Int -> Hat -> String

pprintWithIndentations :: Int -> Int -> String -> Hat -> String

pprintIndent :: Int -> Hat -> String

Simplifiable Hat

Defined in Math.FiniteCategories.Hat

Methods

simplify :: Hat -> Hat

Generic Hat

Defined in Math.FiniteCategories.Hat

Associated Types

type Rep Hat :: Type -> Type

Methods

from :: Hat -> Rep Hat x

to :: Rep Hat x -> Hat

Show Hat

Defined in Math.FiniteCategories.Hat

Methods

showsPrec :: Int -> Hat -> ShowS

show :: Hat -> String

showList :: [Hat] -> ShowS

Eq Hat

Defined in Math.FiniteCategories.Hat

Methods

(==) :: Hat -> Hat -> Bool

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

Category Hat HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

identity :: Hat -> HatOb -> HatAr

ar :: Hat -> HatOb -> HatOb -> Set HatAr

genAr :: Hat -> HatOb -> HatOb -> Set HatAr

decompose :: Hat -> HatAr -> [HatAr]

FiniteCategory Hat HatAr HatOb

Defined in Math.FiniteCategories.Hat

Methods

ob :: Hat -> Set HatOb

type Rep Hat

Defined in Math.FiniteCategories.Hat

type Rep Hat = D1 ('MetaData "Hat" "Math.FiniteCategories.Hat" "FiniteCategories-0.6.0.1-L2v014CZIYe4CTCeXkyH5k" 'False) (C1 ('MetaCons "Hat" 'PrefixI 'False) (U1 :: Type -> Type))