L-trivial semigroups#
- class sage.categories.l_trivial_semigroups.LTrivialSemigroups(base_category)[source]#
Bases:
CategoryWithAxiom
- Commutative_extra_super_categories()[source]#
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]
>>> from sage.all import * >>> Semigroups().LTrivial().Commutative_extra_super_categories() [Category of j trivial semigroups]
- RTrivial_extra_super_categories()[source]#
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]
>>> from sage.all import * >>> Semigroups().LTrivial().RTrivial_extra_super_categories() [Category of j trivial magmas]
- extra_super_categories()[source]#
Implement the fact that a \(L\)-trivial semigroup is \(H\)-trivial.
EXAMPLES:
sage: Semigroups().LTrivial().extra_super_categories() [Category of h trivial semigroups]
>>> from sage.all import * >>> Semigroups().LTrivial().extra_super_categories() [Category of h trivial semigroups]