{I : Type u} →
  [inst : CategoryTheory.Category.{u, u} I] →
    {S X : AlgebraicGeometry.Scheme} →
      {D : CategoryTheory.Functor I AlgebraicGeometry.Scheme} →
        {t : D ⟶ (CategoryTheory.Functor.const I).obj S} →
          {f : X ⟶ S} →
            [∀ (i : I), CompactSpace ↥(D.obj i)] →
              [CategoryTheory.IsCofiltered I] →
                [∀ {i j : I} (f : i ⟶ j), AlgebraicGeometry.IsAffineHom (D.map f)] →
                  AlgebraicGeometry.ExistsHomHomCompEqCompAux D t f → I