Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.covers
∀ {K : CategoryTheory.Precoverage AlgebraicGeometry.Scheme} {X : AlgebraicGeometry.Scheme}
[inst : AlgebraicGeometry.Scheme.JointlySurjective K] (𝒰 : AlgebraicGeometry.Scheme.Cover K X) (x : ↥X),
x ∈ Set.range ⇑(𝒰.f (𝒰.idx x))- Cited by
- 14 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Set.rangestatement · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- TopCatstatement · cited by 1,889
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.affineBasisCover_is_basisproof · cited by 2
- AlgebraicGeometry.Scheme.nonempty_of_isLimitproof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.of_isOpenMapproof · cited by 1
- AlgebraicGeometry.compactSpace_of_universallyClosedproof · cited by 1
- AlgebraicGeometry.Scheme.OpenCover.ext_elemproof · cited by 1
- AlgebraicGeometry.Scheme.Cover.isOpenMap_fromGluedproof · cited by 1
- AlgebraicGeometry.sourceLocalClosure.iff_forall_existsproof · cited by 1
- AlgebraicGeometry.AffineSpace.isIntegralHom_over_iff_isEmptyproof · cited by 0
- AlgebraicGeometry.Scheme.IsGermInjective.of_openCoverproof · cited by 0
- AlgebraicGeometry.Scheme.mem_toGrothendieck_smallPretopologyproof · cited by 0