Transfer of ample-semigroup properties

Characterize which properties of free or left ample semigroups extend to free or left h-adequate and h-Ehresmann semigroups.

Background

The paper develops several finitary results for free left h-Ehresmann monoids, including ideal Howson, finite equationality, and weak coherence, and compares these structures with free ample and free Ehresmann monoids.

It leaves unresolved the broader structural question of which properties known for free or left ample semigroups persist for the corresponding h-adequate or h-Ehresmann classes. This is intentionally open-ended and concerns identifying the scope of the analogy beyond the properties established in the paper.