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

Math.Categories.OrdinalCategory

Description

An OrdinalCategory is a TotalOrder category where the total order is an order induced by ordinal numbers.

Concretely the type parameter must implement the Enum typeclass.

For example, the TotalOrder category induced by (R,<=) is not an OrdinalCategory whereas (N,<=) is.

It induces a non trivial generating set of arrows thanks to the succ function.

Synopsis

newtype OrdinalCategory a = OrdinalCategory (TotalOrder a)
module Math.Categories.TotalOrder

Documentation

newtype OrdinalCategory a Source #

An OrdinalCategory is a TotalOrder where the type a follows the Enum typeclass.

Constructors

OrdinalCategory (TotalOrder a)

Instances

Instances details

PrettyPrint (OrdinalCategory a) Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods pprint :: Int -> OrdinalCategory a -> String Source # pprintWithIndentations :: Int -> Int -> String -> OrdinalCategory a -> String Source # pprintIndent :: Int -> OrdinalCategory a -> String Source #
Simplifiable (OrdinalCategory a) Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods simplify :: OrdinalCategory a -> OrdinalCategory a #
Generic (OrdinalCategory a) Source #
Instance details Defined in Math.Categories.OrdinalCategory Associated Types type Rep (OrdinalCategory a) :: Type -> Type Methods from :: OrdinalCategory a -> Rep (OrdinalCategory a) x to :: Rep (OrdinalCategory a) x -> OrdinalCategory a
Show (OrdinalCategory a) Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods showsPrec :: Int -> OrdinalCategory a -> ShowS show :: OrdinalCategory a -> String showList :: [OrdinalCategory a] -> ShowS
Eq (OrdinalCategory a) Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods (==) :: OrdinalCategory a -> OrdinalCategory a -> Bool (/=) :: OrdinalCategory a -> OrdinalCategory a -> Bool
(Enum a, Ord a) => Category (OrdinalCategory a) (IsSmallerThan a) a Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods identity :: OrdinalCategory a -> a -> IsSmallerThan a Source # ar :: OrdinalCategory a -> a -> a -> Set (IsSmallerThan a) Source # genAr :: OrdinalCategory a -> a -> a -> Set (IsSmallerThan a) Source # decompose :: OrdinalCategory a -> IsSmallerThan a -> [IsSmallerThan a] Source #
(Enum a, Ord a) => HasCoequalizers (OrdinalCategory a) (IsSmallerThan a) a Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods coequalize :: Diagram Parallel ParallelAr ParallelOb (OrdinalCategory a) (IsSmallerThan a) a -> Cocone Parallel ParallelAr ParallelOb (OrdinalCategory a) (IsSmallerThan a) a Source #
(Enum a, Ord a) => HasEqualizers (OrdinalCategory a) (IsSmallerThan a) a Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods equalize :: Diagram Parallel ParallelAr ParallelOb (OrdinalCategory a) (IsSmallerThan a) a -> Cone Parallel ParallelAr ParallelOb (OrdinalCategory a) (IsSmallerThan a) a Source #
(Enum a, Ord a, Eq oIndex) => HasCoproducts (OrdinalCategory a) (IsSmallerThan a) a (OrdinalCategory a) (IsSmallerThan a) a oIndex Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods coproduct :: Diagram (DiscreteCategory oIndex) (DiscreteMorphism oIndex) oIndex (OrdinalCategory a) (IsSmallerThan a) a -> Cocone (DiscreteCategory oIndex) (DiscreteMorphism oIndex) oIndex (OrdinalCategory a) (IsSmallerThan a) a Source #
(Enum a, Ord a, Eq oIndex) => HasProducts (OrdinalCategory a) (IsSmallerThan a) a (OrdinalCategory a) (IsSmallerThan a) a oIndex Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods product :: Diagram (DiscreteCategory oIndex) (DiscreteMorphism oIndex) oIndex (OrdinalCategory a) (IsSmallerThan a) a -> Cone (DiscreteCategory oIndex) (DiscreteMorphism oIndex) oIndex (OrdinalCategory a) (IsSmallerThan a) a Source #
(Enum a, Ord a, Eq mIndex, Eq oIndex) => CocompleteCategory (OrdinalCategory a) (IsSmallerThan a) a (OrdinalCategory a) (IsSmallerThan a) a cIndex mIndex oIndex Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods colimit :: Diagram cIndex mIndex oIndex (OrdinalCategory a) (IsSmallerThan a) a -> Cocone cIndex mIndex oIndex (OrdinalCategory a) (IsSmallerThan a) a Source # coprojectBase :: Diagram cIndex mIndex oIndex (OrdinalCategory a) (IsSmallerThan a) a -> Diagram (OrdinalCategory a) (IsSmallerThan a) a (OrdinalCategory a) (IsSmallerThan a) a Source #
(Enum a, Ord a, Eq mIndex, Eq oIndex) => CompleteCategory (OrdinalCategory a) (IsSmallerThan a) a (OrdinalCategory a) (IsSmallerThan a) a cIndex mIndex oIndex Source #
Instance details Defined in Math.Categories.OrdinalCategory Methods limit :: Diagram cIndex mIndex oIndex (OrdinalCategory a) (IsSmallerThan a) a -> Cone cIndex mIndex oIndex (OrdinalCategory a) (IsSmallerThan a) a Source # projectBase :: Diagram cIndex mIndex oIndex (OrdinalCategory a) (IsSmallerThan a) a -> Diagram (OrdinalCategory a) (IsSmallerThan a) a (OrdinalCategory a) (IsSmallerThan a) a Source #
type Rep (OrdinalCategory a) Source #
Instance details Defined in Math.Categories.OrdinalCategory type Rep (OrdinalCategory a) = D1 ('MetaData "OrdinalCategory" "Math.Categories.OrdinalCategory" "FiniteCategories-0.6.4.0-inplace" 'True) (C1 ('MetaCons "OrdinalCategory" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (TotalOrder a))))

module Math.Categories.TotalOrder