L-trivial semigroups

class sage.categories.l_trivial_semigroups.LTrivialSemigroups(base_category)

Bases: CategoryWithAxiom

Commutative_extra_super_categories()

Implement the fact that a commutative \(R\)-trivial semigroup is \(J\)-trivial.

EXAMPLES:

Sage

sage: Semigroups().LTrivial().Commutative_extra_super_categories()
[Category of j trivial semigroups]

Python

>>> from sage.all import *
>>> Semigroups().LTrivial().Commutative_extra_super_categories()
[Category of j trivial semigroups]

RTrivial_extra_super_categories()

Implement the fact that an \(L\)-trivial and \(R\)-trivial semigroup is \(J\)-trivial.

EXAMPLES:

Sage

sage: Semigroups().LTrivial().RTrivial_extra_super_categories()
[Category of j trivial magmas]

Python

>>> from sage.all import *
>>> Semigroups().LTrivial().RTrivial_extra_super_categories()
[Category of j trivial magmas]

extra_super_categories()

Implement the fact that a \(L\)-trivial semigroup is \(H\)-trivial.

EXAMPLES:

Sage

sage: Semigroups().LTrivial().extra_super_categories()
[Category of h trivial semigroups]

Python

>>> from sage.all import *
>>> Semigroups().LTrivial().extra_super_categories()
[Category of h trivial semigroups]