{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preregular C] →
      [inst_2 : CategoryTheory.FinitaryExtensive C] →
        {F : CategoryTheory.Functor ℕᵒᵖ (CategoryTheory.Sheaf (CategoryTheory.coherentTopology C) (Type v))} →
          (∀ (n : ℕ), CategoryTheory.Sheaf.IsLocallySurjective (F.map (CategoryTheory.homOfLE ⋯).op)) →
            (X : C) →
              (F.obj (Opposite.op 0)).obj.obj (Opposite.op X) →
                (n : ℕ) → (Y : C) × (F.obj (Opposite.op n)).obj.obj (Opposite.op Y)