∀ {𝒮 : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} 𝒮] {𝒳 : CategoryTheory.BasedCategory 𝒮}
  {𝒴 : CategoryTheory.BasedCategory 𝒮} {𝒵 : CategoryTheory.BasedCategory 𝒮} {F G : CategoryTheory.BasedFunctor 𝒳 𝒴}
  (α : F ⟶ G) (H : CategoryTheory.BasedFunctor 𝒴 𝒵) (x : 𝒳.obj),
  𝒵.p.IsHomLift (CategoryTheory.CategoryStruct.id (𝒳.p.obj x)) (H.map (α.app x))