∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  [hasFiniteCoproducts : CategoryTheory.Limits.HasFiniteCoproducts C]
  [hasPullbacksOfInclusions : CategoryTheory.HasPullbacksOfInclusions C],
  (∀ {X Y : C} (c : CategoryTheory.Limits.BinaryCofan X Y) (a : CategoryTheory.Limits.IsColimit c),
      CategoryTheory.IsUniversalColimit c) →
    CategoryTheory.FinitaryPreExtensive C