L-trivial semigroups¶
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class
sage.categories.l_trivial_semigroups.
LTrivialSemigroups
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom
TESTS:
sage: C = Sets.Finite(); C Category of finite sets sage: type(C) <class 'sage.categories.finite_sets.FiniteSets_with_category'> sage: type(C).__base__.__base__ <class 'sage.categories.category_with_axiom.CategoryWithAxiom_singleton'> sage: TestSuite(C).run()
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Commutative_extra_super_categories
()¶ Implement the fact that a commutative \(R\)-trivial semigroup is \(J\)-trivial.
EXAMPLES:
sage: Semigroups().LTrivial().Commutative_extra_super_categories() [Category of j trivial semigroups]
TESTS:
sage: Semigroups().LTrivial().Commutative() is Semigroups().JTrivial().Commutative() True
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RTrivial_extra_super_categories
()¶ Implement the fact that an \(L\)-trivial and \(R\)-trivial semigroup is \(J\)-trivial.
EXAMPLES:
sage: Semigroups().LTrivial().RTrivial_extra_super_categories() [Category of j trivial magmas]
TESTS:
sage: Semigroups().LTrivial().RTrivial() is Semigroups().JTrivial() True
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extra_super_categories
()¶ Implement the fact that a \(L\)-trivial semigroup is \(H\)-trivial.
EXAMPLES:
sage: Semigroups().LTrivial().extra_super_categories() [Category of h trivial semigroups]
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