Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.awayMap_awayToSection_assoc

∀ {σ : Type u_1} {A : Type u} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] {f : A} {m' : ℕ} {g : A} (g_deg : g ∈ 𝒜 m') {x : A} (hx : x = f * g) {Z : CommRingCat}
  (h : (AlgebraicGeometry.Proj 𝒜).presheaf.obj (Opposite.op (AlgebraicGeometry.Proj.basicOpen 𝒜 x)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CommRingCat.ofHom (HomogeneousLocalization.awayMap 𝒜 g_deg hx))
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.awayToSection 𝒜 x) h) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Proj.awayToSection 𝒜 f)
      (CategoryTheory.CategoryStruct.comp ((AlgebraicGeometry.Proj 𝒜).presheaf.map (CategoryTheory.homOfLE ⋯).op) h)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

0 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing