∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {ι : Type u_1} {P : ι → CategoryTheory.MorphismProperty C}
  {κ : Cardinal.{w}} [Fact κ.IsRegular],
  (∀ (i : ι), (P i).HasCardinalLT κ) → HasCardinalLT ι κ → (⨆ i, P i).HasCardinalLT κ