Math.Categories.OrdinalCategory

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.

Documentation

newtype OrdinalCategory a

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

Constructors

OrdinalCategory (TotalOrder a)

Instances

Eq (OrdinalCategory a)

Defined in Math.Categories.OrdinalCategory

Methods

(==) :: OrdinalCategory a -> OrdinalCategory a -> Bool

(/=) :: OrdinalCategory a -> OrdinalCategory a -> Bool

Show (OrdinalCategory a)

Defined in Math.Categories.OrdinalCategory

Methods

showsPrec :: Int -> OrdinalCategory a -> ShowS

show :: OrdinalCategory a -> String

showList :: [OrdinalCategory a] -> ShowS

Show a => PrettyPrint (OrdinalCategory a)

Defined in Math.Categories.OrdinalCategory

Methods

pprint :: OrdinalCategory a -> String

(Enum a, Ord a) => Category (OrdinalCategory a) (IsSmallerThan a) a

Defined in Math.Categories.OrdinalCategory

Methods

identity :: OrdinalCategory a -> a -> IsSmallerThan a

ar :: OrdinalCategory a -> a -> a -> Set (IsSmallerThan a)

genAr :: OrdinalCategory a -> a -> a -> Set (IsSmallerThan a)

decompose :: OrdinalCategory a -> IsSmallerThan a -> [IsSmallerThan a]

module Math.Categories.TotalOrder