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]