Sort u →
  {C : Type u_1} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      {W₁ W₂ : CategoryTheory.MorphismProperty C} →
        {X Y : C} →
          {f : X ⟶ Y} →
            W₁.MapFactorizationData W₂ f →
              {C' : Type u_1} →
                [inst' : CategoryTheory.Category.{v_1, u_1} C'] →
                  {W₁' W₂' : CategoryTheory.MorphismProperty C'} →
                    {X' Y' : C'} → {f' : X' ⟶ Y'} → W₁'.MapFactorizationData W₂' f' → Sort u