Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Proj.res_apply
∀ {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] {U V : (TopologicalSpace.Opens ↑(ProjectiveSpectrum.top 𝒜))ᵒᵖ} (i : V ⟶ U)
(s : ↑((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).obj.obj V)) (x : ↥(Opposite.unop U)),
↑((CategoryTheory.ConcreteCategory.hom ((AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf 𝒜).obj.map i)) s)
x =
↑s (i.unop x)- 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.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- RingHomstatement · cited by 10,189
- CategoryTheory.Functor.mapstatement · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- Opposite.unopstatement and proof · cited by 2,231
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.homogeneousLocalizationToStalk_stalkToFiberRingHomproof · cited by 0