Morita equivalence based on Morita context for arbitrary semigroups

In this paper, we study the Morita context for arbitrary semigroups. We prove that, for two semigroups S and T, if there exists a Morita context $(S, T, P, Q, \tau, \mu)$ (not necessary unital) such that the maps $\tau$ and $\mu$ are surjective, the categories U S -FAct and U T -FAct are equivalent. Using this result, we generalize Theorem 2 in [2] to arbitrary semigroups. Finally, we give a characterization of Morita context for semigroups.