Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Proj.ext
∀ {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] {V : (TopologicalSpace.Opens ↑(ProjectiveSpectrum.top 𝒜))ᵒᵖ}
(s t : ↑((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).obj.obj V)), ↑s = ↑t → s = t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- Opposite.unopstatement · cited by 2,231
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- CommRingCat.carrierstatement and proof · cited by 1,096
- SetLikestatement and proof · cited by 1,084
- CategoryTheory.Presheaf.IsSheafstatement · cited by 991
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.ext_iffproof · cited by 0