Embedding semigroups into semigroups with countability index two.
The original version of the article was published in Central European Journal of Mathematics, 2007, 5(1), 181–200, DOI: 10.2478/s11533-006-0036-3. Unfortunately, the original version of this article contains a mistake: in Theorem 5.2 only conditions (i) and (ii) (and not (iii)) are equivalent. We correct the theorem and its proof.
The paper contains characterizations of generators and cyclic projective generators in the category of ordered right acts over an ordered monoid.