Math.FiniteCategories.FullSubcategory

Selecting a FullSubcategory in a Category yields a FiniteCategory.

We have to forget the generating set of morphisms of the original Category as the generators are not always inheritable (see for example the full subcategory of Square containing the objects A and D).

If the generators are inheritable, you can use the constructor InheritedFullSubcategory to inherit the generators of the original Category.

Documentation

data FullSubcategory c m o

A FullSubcategory needs an original category and a set of objects to select in the category.

The generators are forgotten, use InheritedFullSubcategory if the generators are inheritable.

Constructors

FullSubcategory c (Set o)

Instances

(PrettyPrint c, PrettyPrint o, Eq o) => PrettyPrint (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

pprint :: Int -> FullSubcategory c m o -> String

pprintWithIndentations :: Int -> Int -> String -> FullSubcategory c m o -> String

pprintIndent :: Int -> FullSubcategory c m o -> String

(Simplifiable c, Simplifiable o, Eq o) => Simplifiable (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

simplify :: FullSubcategory c m o -> FullSubcategory c m o

Generic (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Associated Types

type Rep (FullSubcategory c m o) :: Type -> Type

Methods

from :: FullSubcategory c m o -> Rep (FullSubcategory c m o) x

to :: Rep (FullSubcategory c m o) x -> FullSubcategory c m o

(Show c, Show o) => Show (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

showsPrec :: Int -> FullSubcategory c m o -> ShowS

show :: FullSubcategory c m o -> String

showList :: [FullSubcategory c m o] -> ShowS

(Eq c, Eq o) => Eq (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

(==) :: FullSubcategory c m o -> FullSubcategory c m o -> Bool

(/=) :: FullSubcategory c m o -> FullSubcategory c m o -> Bool

(Category c m o, Eq o) => Category (FullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

identity :: FullSubcategory c m o -> o -> m

ar :: FullSubcategory c m o -> o -> o -> Set m

genAr :: FullSubcategory c m o -> o -> o -> Set m

decompose :: FullSubcategory c m o -> m -> [m]

(Category c m o, Eq o) => FiniteCategory (FullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

ob :: FullSubcategory c m o -> Set o

type Rep (FullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

type Rep (FullSubcategory c m o) = D1 ('MetaData "FullSubcategory" "Math.FiniteCategories.FullSubcategory" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "FullSubcategory" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 c) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Set o))))

data InheritedFullSubcategory c m o

An InheritedFullSubcategory is a FullSubcategory where the generators are the same as in the original Category.

Constructors

InheritedFullSubcategory c (Set o)

Instances

(PrettyPrint c, PrettyPrint o, Eq o) => PrettyPrint (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

pprint :: Int -> InheritedFullSubcategory c m o -> String

pprintWithIndentations :: Int -> Int -> String -> InheritedFullSubcategory c m o -> String

pprintIndent :: Int -> InheritedFullSubcategory c m o -> String

(Simplifiable c, Simplifiable o, Eq o) => Simplifiable (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

simplify :: InheritedFullSubcategory c m o -> InheritedFullSubcategory c m o

Generic (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Associated Types

type Rep (InheritedFullSubcategory c m o) :: Type -> Type

Methods

from :: InheritedFullSubcategory c m o -> Rep (InheritedFullSubcategory c m o) x

to :: Rep (InheritedFullSubcategory c m o) x -> InheritedFullSubcategory c m o

(Show c, Show o) => Show (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

showsPrec :: Int -> InheritedFullSubcategory c m o -> ShowS

show :: InheritedFullSubcategory c m o -> String

showList :: [InheritedFullSubcategory c m o] -> ShowS

(Eq c, Eq o) => Eq (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

Methods

(==) :: InheritedFullSubcategory c m o -> InheritedFullSubcategory c m o -> Bool

(/=) :: InheritedFullSubcategory c m o -> InheritedFullSubcategory c m o -> Bool

(Category c m o, Eq o) => Category (InheritedFullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

identity :: InheritedFullSubcategory c m o -> o -> m

ar :: InheritedFullSubcategory c m o -> o -> o -> Set m

genAr :: InheritedFullSubcategory c m o -> o -> o -> Set m

decompose :: InheritedFullSubcategory c m o -> m -> [m]

(Category c m o, Eq o) => FiniteCategory (InheritedFullSubcategory c m o) m o

Defined in Math.FiniteCategories.FullSubcategory

Methods

ob :: InheritedFullSubcategory c m o -> Set o

type Rep (InheritedFullSubcategory c m o)

Defined in Math.FiniteCategories.FullSubcategory

type Rep (InheritedFullSubcategory c m o) = D1 ('MetaData "InheritedFullSubcategory" "Math.FiniteCategories.FullSubcategory" "FiniteCategories-0.6.4.0-inplace" 'False) (C1 ('MetaCons "InheritedFullSubcategory" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 c) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Set o))))