Finite sets¶
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class
sage.categories.finite_sets.
FiniteSets
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
The category of finite sets.
EXAMPLES:
sage: C = FiniteSets(); C Category of finite sets sage: C.super_categories() [Category of sets] sage: C.all_super_categories() [Category of finite sets, Category of sets, Category of sets with partial maps, Category of objects] sage: C.example() NotImplemented
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class
Algebras
(category, *args)¶ Bases:
sage.categories.algebra_functor.AlgebrasCategory
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extra_super_categories
()¶ EXAMPLES:
sage: FiniteSets().Algebras(QQ).extra_super_categories() [Category of finite dimensional vector spaces with basis over Rational Field]
This implements the fact that the algebra of a finite set is finite dimensional:
sage: FiniteMonoids().Algebras(QQ).is_subcategory(AlgebrasWithBasis(QQ).FiniteDimensional()) True
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class
ParentMethods
¶ Bases:
object
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is_finite
()¶ Return
True
sinceself
is finite.EXAMPLES:
sage: C = FiniteEnumeratedSets().example() sage: C.is_finite() True
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class
Subquotients
(category, *args)¶ Bases:
sage.categories.subquotients.SubquotientsCategory
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extra_super_categories
()¶ EXAMPLES:
sage: FiniteSets().Subquotients().extra_super_categories() [Category of finite sets]
This implements the fact that a subquotient (and therefore a quotient or subobject) of a finite set is finite:
sage: FiniteSets().Subquotients().is_subcategory(FiniteSets()) True sage: FiniteSets().Quotients ().is_subcategory(FiniteSets()) True sage: FiniteSets().Subobjects ().is_subcategory(FiniteSets()) True
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class