Some Galois connections arising from Morita contexts of semigroups

We show that a unitary surjective Morita context connecting two semigroups yields Galois connections between certain lattices of compatible relations whenever either semigroup has common weak local units. In the event both semigroups have common weak local units, we obtain mutually inverse lattice isomorphisms that preserve reflexivity, symmetricity and transitivity between the lattices of compatible relations on the semigroups.