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

Math.FiniteCategories.Hat

Description

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

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

Synopsis

data HatOb
- = HatA
- | HatB
- | HatC
data HatAr
- = HatIdA
- | HatIdB
- | HatIdC
- | HatF
- | HatG
data Hat = Hat

Documentation

data HatOb Source #

Objects of the Hat category.

Constructors

HatA
HatB
HatC

Instances

Instances details

PrettyPrint HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods pprint :: Int -> HatOb -> String Source # pprintWithIndentations :: Int -> Int -> String -> HatOb -> String Source # pprintIndent :: Int -> HatOb -> String Source #
Simplifiable HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods simplify :: HatOb -> HatOb #
Generic HatOb Source #
Instance details 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 Source #
Instance details Defined in Math.FiniteCategories.Hat Methods showsPrec :: Int -> HatOb -> ShowS show :: HatOb -> String showList :: [HatOb] -> ShowS
Eq HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods (==) :: HatOb -> HatOb -> Bool (/=) :: HatOb -> HatOb -> Bool
Morphism HatAr HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods (@) :: HatAr -> HatAr -> HatAr Source # (@?) :: HatAr -> HatAr -> Maybe HatAr Source # source :: HatAr -> HatOb Source # target :: HatAr -> HatOb Source #
Category Hat HatAr HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods identity :: Hat -> HatOb -> HatAr Source # ar :: Hat -> HatOb -> HatOb -> Set HatAr Source # genAr :: Hat -> HatOb -> HatOb -> Set HatAr Source # decompose :: Hat -> HatAr -> [HatAr] Source #
FiniteCategory Hat HatAr HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods ob :: Hat -> Set HatOb Source #
type Rep HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat type Rep HatOb = D1 ('MetaData "HatOb" "Math.FiniteCategories.Hat" "FiniteCategories-0.6.4.0-inplace" '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 Source #

Morphisms of the Hat category.

Constructors

HatIdA
HatIdB
HatIdC
HatF
HatG

Instances

Instances details

PrettyPrint HatAr Source #
Instance details Defined in Math.FiniteCategories.Hat Methods pprint :: Int -> HatAr -> String Source # pprintWithIndentations :: Int -> Int -> String -> HatAr -> String Source # pprintIndent :: Int -> HatAr -> String Source #
Simplifiable HatAr Source #
Instance details Defined in Math.FiniteCategories.Hat Methods simplify :: HatAr -> HatAr #
Generic HatAr Source #
Instance details 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 Source #
Instance details Defined in Math.FiniteCategories.Hat Methods showsPrec :: Int -> HatAr -> ShowS show :: HatAr -> String showList :: [HatAr] -> ShowS
Eq HatAr Source #
Instance details Defined in Math.FiniteCategories.Hat Methods (==) :: HatAr -> HatAr -> Bool (/=) :: HatAr -> HatAr -> Bool
Morphism HatAr HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods (@) :: HatAr -> HatAr -> HatAr Source # (@?) :: HatAr -> HatAr -> Maybe HatAr Source # source :: HatAr -> HatOb Source # target :: HatAr -> HatOb Source #
Category Hat HatAr HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods identity :: Hat -> HatOb -> HatAr Source # ar :: Hat -> HatOb -> HatOb -> Set HatAr Source # genAr :: Hat -> HatOb -> HatOb -> Set HatAr Source # decompose :: Hat -> HatAr -> [HatAr] Source #
FiniteCategory Hat HatAr HatOb Source #
Instance details Defined in Math.FiniteCategories.Hat Methods ob :: Hat -> Set HatOb Source #
type Rep HatAr Source #
Instance details Defined in Math.FiniteCategories.Hat type Rep HatAr = D1 ('MetaData "HatAr" "Math.FiniteCategories.Hat" "FiniteCategories-0.6.4.0-inplace" '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 Source #

The Hat category.

Constructors

Hat

Instances

Instances details

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