Theorems · Theorem · algebraic geometry
AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_surjective
∀ {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} {m : ℕ},
f ∈ 𝒜 m →
0 < m →
Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec 𝒜 f))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Functor.objstatement · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- TopCatstatement · cited by 1,889
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_bijectiveproof · cited by 0