Lattice isomorphisms of free products of inverse semigroups (Q797704)

Let S, T, W be inverse semigroups; let S inv T be the free product of S and T in the category of inverse semigroups. Denote by \({\mathcal L}(W)\) the lattice of inverse subsemigroups of the semigroup W. The main result is the following: any isomorphism of \({\mathcal L}(S inv T)\) upon the lattice \({\mathcal L}(W)\) is induced by a unique isomorphism of S inv T upon W.