∀ {S : AlgebraicGeometry.Scheme} {J : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} J]
  (F : CategoryTheory.Functor J (CategoryTheory.Over S))
  [∀ {i j : J} (f : i ⟶ j), AlgebraicGeometry.IsOpenImmersion (F.map f).left]
  [(F.comp ((CategoryTheory.Over.forget S).comp AlgebraicGeometry.Scheme.forget)).IsLocallyDirected] [Quiver.IsThin J]
  [Small.{u, u_1} J], CategoryTheory.Limits.HasColimit F