∀ {J : Type v} [inst : CategoryTheory.SmallCategory J] {F : CategoryTheory.Functor J CategoryTheory.Cat}
  (X Y : CategoryTheory.Limits.limit (F.comp CategoryTheory.Cat.objects)) (j : J),
  (CategoryTheory.Cat.HasLimits.homDiagram X Y).obj j =
    (CategoryTheory.Limits.limit.π (F.comp CategoryTheory.Cat.objects) j X ⟶
      CategoryTheory.Limits.limit.π (F.comp CategoryTheory.Cat.objects) j Y)