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

Math.Categories.Galaxy

Description

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.

Synopsis

data StarIdentity a = StarIdentity a
data Galaxy a = Galaxy

Documentation

data StarIdentity a Source #

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

Constructors

StarIdentity a

Instances

Instances details

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

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

Constructors

Galaxy

Instances

Instances details

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