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

Math.FiniteCategories.Parallel

Description

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

Synopsis

data ParallelOb
- = ParallelA
- | ParallelB
data ParallelAr
- = ParallelIdA
- | ParallelIdB
- | ParallelF
- | ParallelG
data Parallel = Parallel

Documentation

data ParallelOb Source #

Objects of the Parallel category.

Constructors

ParallelA
ParallelB

Instances

Instances details

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

Morphisms of the Parallel category.

Constructors

ParallelIdA
ParallelIdB
ParallelF
ParallelG

Instances

Instances details

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

The Parallel category.

Constructors

Parallel

Instances

Instances details

PrettyPrint Parallel Source #
Instance details Defined in Math.FiniteCategories.Parallel Methods pprint :: Int -> Parallel -> String Source # pprintWithIndentations :: Int -> Int -> String -> Parallel -> String Source # pprintIndent :: Int -> Parallel -> String Source #
Simplifiable Parallel Source #
Instance details Defined in Math.FiniteCategories.Parallel Methods simplify :: Parallel -> Parallel #
Generic Parallel Source #
Instance details 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 Source #
Instance details Defined in Math.FiniteCategories.Parallel Methods showsPrec :: Int -> Parallel -> ShowS show :: Parallel -> String showList :: [Parallel] -> ShowS
Eq Parallel Source #
Instance details Defined in Math.FiniteCategories.Parallel Methods (==) :: Parallel -> Parallel -> Bool (/=) :: Parallel -> Parallel -> Bool
Category Parallel ParallelAr ParallelOb Source #
Instance details Defined in Math.FiniteCategories.Parallel Methods identity :: Parallel -> ParallelOb -> ParallelAr Source # ar :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr Source # genAr :: Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr Source # decompose :: Parallel -> ParallelAr -> [ParallelAr] Source #
FiniteCategory Parallel ParallelAr ParallelOb Source #
Instance details Defined in Math.FiniteCategories.Parallel Methods ob :: Parallel -> Set ParallelOb Source #
type Rep Parallel Source #
Instance details 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))