∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] (f : A)
  (U :
    (TopologicalSpace.Opens
        ↑↑(AlgebraicGeometry.Spec.locallyRingedSpaceObj
                { carrier := HomogeneousLocalization.Away 𝒜 f,
                  commRing := HomogeneousLocalization.homogeneousLocalizationCommRing }).toPresheafedSpace)ᵒᵖ)
  {Z : CommRingCat}
  (h :
    ((TopCat.Presheaf.pushforward CommRingCat (AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f).base).obj
            ((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯).presheaf).obj
        U ⟶
      Z),
  CategoryTheory.CategoryStruct.comp
      (AlgebraicGeometry.Scheme.ΓSpecIso
          { carrier := HomogeneousLocalization.Away 𝒜 f,
            commRing := HomogeneousLocalization.homogeneousLocalizationCommRing }).inv
      (CategoryTheory.CategoryStruct.comp
        ((AlgebraicGeometry.Spec.locallyRingedSpaceObj
                { carrier := HomogeneousLocalization.Away 𝒜 f,
                  commRing := HomogeneousLocalization.homogeneousLocalizationCommRing }).presheaf.map
          (CategoryTheory.homOfLE ⋯).op)
        (CategoryTheory.CategoryStruct.comp ((AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f).c.app U) h)) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ 𝒜 f)
      (CategoryTheory.CategoryStruct.comp
        (((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯).presheaf.map (CategoryTheory.homOfLE ⋯).op) h)