Math.Categories.Galaxy

The Galaxy category has every objects and no morphism other than identities.

It is called Galaxy because its underlying graph is composed of a lot of points with no arrow between them.

It is the biggest DiscreteCategory.

Documentation

data StarIdentity a

StarIdentity is the identity of a star (an object) in a Galaxy.

Constructors

StarIdentity a

Instances

Eq a => Eq (StarIdentity a)

Defined in Math.Categories.Galaxy

Methods

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

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

Show a => Show (StarIdentity a)

Defined in Math.Categories.Galaxy

Methods

showsPrec :: Int -> StarIdentity a -> ShowS

show :: StarIdentity a -> String

showList :: [StarIdentity a] -> ShowS

PrettyPrint a => PrettyPrint (StarIdentity a)

Defined in Math.Categories.Galaxy

Methods

pprint :: StarIdentity a -> String

Eq a => Morphism (StarIdentity a) a

Defined in Math.Categories.Galaxy

Methods

(@?) :: StarIdentity a -> StarIdentity a -> Maybe (StarIdentity a)

source :: StarIdentity a -> a

target :: StarIdentity a -> a

Eq a => Category (Galaxy a) (StarIdentity a) a

Defined in Math.Categories.Galaxy

Methods

identity :: Galaxy a -> a -> StarIdentity a

ar :: Galaxy a -> a -> a -> Set (StarIdentity a)

genAr :: Galaxy a -> a -> a -> Set (StarIdentity a)

decompose :: Galaxy a -> StarIdentity a -> [StarIdentity a]

data Galaxy a

The Galaxy category has every objects and no morphism other than identities.

Constructors

Galaxy

Instances

Eq (Galaxy a)

Defined in Math.Categories.Galaxy

Methods

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

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

Show (Galaxy a)

Defined in Math.Categories.Galaxy

Methods

showsPrec :: Int -> Galaxy a -> ShowS

show :: Galaxy a -> String

showList :: [Galaxy a] -> ShowS

PrettyPrint (Galaxy a)

Defined in Math.Categories.Galaxy

Methods

pprint :: Galaxy a -> String

Eq a => Category (Galaxy a) (StarIdentity a) a

Defined in Math.Categories.Galaxy

Methods

identity :: Galaxy a -> a -> StarIdentity a

ar :: Galaxy a -> a -> a -> Set (StarIdentity a)

genAr :: Galaxy a -> a -> a -> Set (StarIdentity a)

decompose :: Galaxy a -> StarIdentity a -> [StarIdentity a]