Epimorphisms, dominions and semigroups (Q1078335)

Several results and counterexamples on questions of the form, if A and B are closely related semigroups and A is absolutely closed or saturated or epics from A are surjective, does B have that property. For instance, adjoining a unity preserves absolute closedness; it is not known if it preserves saturation, though various side conditions will make it do so.