The group of strong Galois objects associated to a cocommutative Hopf   quasigroup
  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. 
J.N. Alonso \'Alvarez, J.M. Fern\'andez Vilaboa and R. Gonz\'alez   Rodr\'iguez
math.RA