∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {S : AlgebraicGeometry.Scheme} {𝒰 : S.OpenCover}
  [inst : CategoryTheory.Category.{u_3, u_2} 𝒰.I₀] [inst_1 : AlgebraicGeometry.Scheme.Cover.LocallyDirected 𝒰]
  {i j : 𝒰.I₀} (hij : i ⟶ j), P.HasPullbacksAlong (AlgebraicGeometry.Scheme.Cover.trans 𝒰 hij)