∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] {F : CategoryTheory.Functor C FintypeCat} {G : Type u_1}
  [inst_1 : Group G] [inst_2 : (X : C) → MulAction G (F.obj X).carrier],
  (∀ (g : G) {X Y : C} (f : X ⟶ Y) (x : (F.obj X).carrier),
      (CategoryTheory.ConcreteCategory.hom (F.map f)) (g • x) = g • (CategoryTheory.ConcreteCategory.hom (F.map f)) x) →
    CategoryTheory.PreGaloisCategory.IsNaturalSMul F G