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

PrettyPrint a => PrettyPrint (StarIdentity a)

Defined in Math.Categories.Galaxy

Methods

pprint :: Int -> StarIdentity a -> String

pprintWithIndentations :: Int -> Int -> String -> StarIdentity a -> String

pprintIndent :: Int -> StarIdentity a -> String

Simplifiable a => Simplifiable (StarIdentity a)

Defined in Math.Categories.Galaxy

Methods

simplify :: StarIdentity a -> StarIdentity a

Generic (StarIdentity a)

Defined in Math.Categories.Galaxy

Associated Types

type Rep (StarIdentity a) :: Type -> Type

Methods

from :: StarIdentity a -> Rep (StarIdentity a) x

to :: Rep (StarIdentity a) x -> StarIdentity a

Show a => Show (StarIdentity a)

Defined in Math.Categories.Galaxy

Methods

showsPrec :: Int -> StarIdentity a -> ShowS

show :: StarIdentity a -> String

showList :: [StarIdentity a] -> ShowS

Eq a => Eq (StarIdentity a)

Defined in Math.Categories.Galaxy

Methods

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

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

Morphism (StarIdentity a) a

Defined in Math.Categories.Galaxy

Methods

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

(@?) :: 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]

type Rep (StarIdentity a)

Defined in Math.Categories.Galaxy

type Rep (StarIdentity a) = D1 ('MetaData "StarIdentity" "Math.Categories.Galaxy" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "StarIdentity" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

data Galaxy a

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

Constructors

Galaxy

Instances

PrettyPrint (Galaxy a)

Defined in Math.Categories.Galaxy

Methods

pprint :: Int -> Galaxy a -> String

pprintWithIndentations :: Int -> Int -> String -> Galaxy a -> String

pprintIndent :: Int -> Galaxy a -> String

Simplifiable (Galaxy a)

Defined in Math.Categories.Galaxy

Methods

simplify :: Galaxy a -> Galaxy a

Generic (Galaxy a)

Defined in Math.Categories.Galaxy

Associated Types

type Rep (Galaxy a) :: Type -> Type

Methods

from :: Galaxy a -> Rep (Galaxy a) x

to :: Rep (Galaxy a) x -> Galaxy a

Show (Galaxy a)

Defined in Math.Categories.Galaxy

Methods

showsPrec :: Int -> Galaxy a -> ShowS

show :: Galaxy a -> String

showList :: [Galaxy a] -> ShowS

Eq (Galaxy a)

Defined in Math.Categories.Galaxy

Methods

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

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

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]

type Rep (Galaxy a)

Defined in Math.Categories.Galaxy

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