∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {W₁ W₂ : CategoryTheory.MorphismProperty C}
  (data : W₁.FunctorialFactorizationData W₂) (J : Type u_2) [inst_1 : CategoryTheory.Category.{v_2, u_2} J]
  {X Y : CategoryTheory.Arrow (CategoryTheory.Functor J C)} (τ : X ⟶ Y) (j : J),
  ((CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory.Z data J).map τ).app j =
    data.mapZ { left := τ.left.app j, right := τ.right.app j, w := ⋯ }