  Let H be a cocommutative faithfully flat Hopf quasigroup in a strict
symmetric monoidal category with equalizers. In this paper we introduce the
notion of (strong) Galois H-object and we prove that the set of isomorphism
classes of (strong) Galois H-objects is a (group) monoid which coincides, in
the Hopf algebra setting, with the Galois group of H-Galois objects introduced
by Chase and Sweedler.
