∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] [inst_1 : CategoryTheory.GaloisCategory C]
  (F : CategoryTheory.Functor C FintypeCat) {A B : CategoryTheory.PreGaloisCategory.PointedGaloisObject F} (f : A ⟶ B),
  (CategoryTheory.PreGaloisCategory.autGaloisSystem F).map f =
    GrpCat.ofHom (CategoryTheory.PreGaloisCategory.autMapHom f.val)