A general setting for Morita equivalence of semigroups

joint work with Valdis Laan) Recently, a satisfactory theory of Morita equivalence could be developed for semigroups with local units, where this notion can be treated by using Morita contexts. Now we investigate what can be done in a much more general setting. In particular, our results go beyond factorisable semigroups, which is a natural borderline for the so-called strong Morita equivalence.