Math.FiniteCategories.Parallel

The Parallel category contains two objects A and B and two morphisms F : A -> B and G : A -> B.

Documentation

data ParallelOb

Objects of the Parallel category.

Constructors

ParallelA

ParallelB

Instances

PrettyPrint ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

pprint :: Int -> ParallelOb -> String

pprintWithIndentations :: Int -> Int -> String -> ParallelOb -> String

pprintIndent :: Int -> ParallelOb -> String

Simplifiable ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

simplify :: ParallelOb -> ParallelOb

Generic ParallelOb

Defined in Math.FiniteCategories.Parallel

Associated Types

type Rep ParallelOb :: Type -> Type

Methods

from :: ParallelOb -> Rep ParallelOb x

to :: Rep ParallelOb x -> ParallelOb

Show ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

showsPrec :: Int -> ParallelOb -> ShowS

show :: ParallelOb -> String

showList :: [ParallelOb] -> ShowS

Eq ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

(==) :: ParallelOb -> ParallelOb -> Bool

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

Morphism ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

(@) :: ParallelAr -> ParallelAr -> ParallelAr

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

source :: ParallelAr -> ParallelOb

target :: ParallelAr -> ParallelOb

Category Parallel ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

identity :: Parallel -> ParallelOb -> ParallelAr

ar :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr

genAr :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr

decompose :: Parallel -> ParallelAr -> [ParallelAr]

FiniteCategory Parallel ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

ob :: Parallel -> Set ParallelOb

type Rep ParallelOb

Defined in Math.FiniteCategories.Parallel

type Rep ParallelOb = D1 ('MetaData "ParallelOb" "Math.FiniteCategories.Parallel" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "ParallelA" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "ParallelB" 'PrefixI 'False) (U1 :: Type -> Type))

data ParallelAr

Morphisms of the Parallel category.

Constructors

ParallelIdA

ParallelIdB

ParallelF

ParallelG

Instances

PrettyPrint ParallelAr

Defined in Math.FiniteCategories.Parallel

Methods

pprint :: Int -> ParallelAr -> String

pprintWithIndentations :: Int -> Int -> String -> ParallelAr -> String

pprintIndent :: Int -> ParallelAr -> String

Simplifiable ParallelAr

Defined in Math.FiniteCategories.Parallel

Methods

simplify :: ParallelAr -> ParallelAr

Generic ParallelAr

Defined in Math.FiniteCategories.Parallel

Associated Types

type Rep ParallelAr :: Type -> Type

Methods

from :: ParallelAr -> Rep ParallelAr x

to :: Rep ParallelAr x -> ParallelAr

Show ParallelAr

Defined in Math.FiniteCategories.Parallel

Methods

showsPrec :: Int -> ParallelAr -> ShowS

show :: ParallelAr -> String

showList :: [ParallelAr] -> ShowS

Eq ParallelAr

Defined in Math.FiniteCategories.Parallel

Methods

(==) :: ParallelAr -> ParallelAr -> Bool

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

Morphism ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

(@) :: ParallelAr -> ParallelAr -> ParallelAr

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

source :: ParallelAr -> ParallelOb

target :: ParallelAr -> ParallelOb

Category Parallel ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

identity :: Parallel -> ParallelOb -> ParallelAr

ar :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr

genAr :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr

decompose :: Parallel -> ParallelAr -> [ParallelAr]

FiniteCategory Parallel ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

ob :: Parallel -> Set ParallelOb

type Rep ParallelAr

Defined in Math.FiniteCategories.Parallel

type Rep ParallelAr = D1 ('MetaData "ParallelAr" "Math.FiniteCategories.Parallel" "FiniteCategories-0.6.4.0-inplace" 'False) ((C1 ('MetaCons "ParallelIdA" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "ParallelIdB" 'PrefixI 'False) (U1 :: Type -> Type)) :+: (C1 ('MetaCons "ParallelF" 'PrefixI 'False) (U1 :: Type -> Type) :+: C1 ('MetaCons "ParallelG" 'PrefixI 'False) (U1 :: Type -> Type)))

data Parallel

The Parallel category.

Constructors

Parallel

Instances

PrettyPrint Parallel

Defined in Math.FiniteCategories.Parallel

Methods

pprint :: Int -> Parallel -> String

pprintWithIndentations :: Int -> Int -> String -> Parallel -> String

pprintIndent :: Int -> Parallel -> String

Simplifiable Parallel

Defined in Math.FiniteCategories.Parallel

Methods

simplify :: Parallel -> Parallel

Generic Parallel

Defined in Math.FiniteCategories.Parallel

Associated Types

type Rep Parallel :: Type -> Type

Methods

from :: Parallel -> Rep Parallel x

to :: Rep Parallel x -> Parallel

Show Parallel

Defined in Math.FiniteCategories.Parallel

Methods

showsPrec :: Int -> Parallel -> ShowS

show :: Parallel -> String

showList :: [Parallel] -> ShowS

Eq Parallel

Defined in Math.FiniteCategories.Parallel

Methods

(==) :: Parallel -> Parallel -> Bool

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

Category Parallel ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

identity :: Parallel -> ParallelOb -> ParallelAr

ar :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr

genAr :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr

decompose :: Parallel -> ParallelAr -> [ParallelAr]

FiniteCategory Parallel ParallelAr ParallelOb

Defined in Math.FiniteCategories.Parallel

Methods

ob :: Parallel -> Set ParallelOb

type Rep Parallel

Defined in Math.FiniteCategories.Parallel

type Rep Parallel = D1 ('MetaData "Parallel" "Math.FiniteCategories.Parallel" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "Parallel" 'PrefixI 'False) (U1 :: Type -> Type))