Theorems · Theorem · algebraic geometry
AlgebraicGeometry.stalkToFiberRingHom_homogeneousLocalizationToStalk
∀ {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] (x : ↑(ProjectiveSpectrum.top 𝒜))
(z : HomogeneousLocalization.AtPrime 𝒜 x.asHomogeneousIdeal.toIdeal),
(CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.stalkToFiberRingHom 𝒜 x))
(AlgebraicGeometry.homogeneousLocalizationToStalk 𝒜 x z) =
z- Cited by
- 0 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CategoryTheory.Functor.objproof · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- Opposite.unopproof · cited by 2,231
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CommRingCat.carrierstatement and proof · cited by 1,096
- SetLikestatement and proof · cited by 1,084
- Ideal.primeComplstatement and proof · cited by 462
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.stalkIso'proof · cited by 7