∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (F : CategoryTheory.Functor C FintypeCat)
  [inst_1 : CategoryTheory.GaloisCategory C] [CategoryTheory.PreGaloisCategory.FiberFunctor F],
  (CategoryTheory.PreGaloisCategory.functorToAction F).PreservesMonomorphisms