∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J] {K : CategoryTheory.Functor J C}
  {F : CategoryTheory.Functor C D},
  (∀ {c : CategoryTheory.Limits.Cocone K} (hc : CategoryTheory.Limits.IsColimit c),
      Nonempty (CategoryTheory.Limits.IsColimit (F.mapCocone c))) →
    CategoryTheory.Limits.PreservesColimit K F