L-trivial semigroups

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()
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
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
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]