Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isLocallyArtinian_iff_openCover
∀ {X : AlgebraicGeometry.Scheme} (𝒰 : X.OpenCover),
AlgebraicGeometry.IsLocallyArtinian X ↔ ∀ (i : 𝒰.I₀), AlgebraicGeometry.IsLocallyArtinian (𝒰.X i)- Defined in
- Mathlib.AlgebraicGeometry.Artinian
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 162 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.coeproof · cited by 62,936
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- IsOpenproof · cited by 2,400
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- AlgebraicGeometry.PresheafedSpace.Hom.baseproof · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomproof · cited by 995
- AlgebraicGeometry.Scheme.Hom.toLRSHom'proof · cited by 895
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsLocallyArtinian.of_locallyQuasiFiniteproof · cited by 2
- AlgebraicGeometry.isLocallyArtinian_iff_of_isOpenCoverproof · cited by 0