Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Cover.exists_eq
∀ {K : CategoryTheory.Precoverage AlgebraicGeometry.Scheme} {X : AlgebraicGeometry.Scheme}
[AlgebraicGeometry.Scheme.JointlySurjective K] (𝒰 : AlgebraicGeometry.Scheme.Cover K X) (x : ↥X), ∃ i y, (𝒰.f i) y = x- Cited by
- 12 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · 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 by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.idxproof · cited by 28
- AlgebraicGeometry.Scheme.Cover.coversproof · cited by 14
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.IsReduced.of_openCoverproof · cited by 2
- AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpenproof · cited by 2
- AlgebraicGeometry.isLocallyArtinian_iff_openCoverproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_applyproof · cited by 2
- AlgebraicGeometry.Scheme.Cover.iUnion_rangeproof · cited by 2
- AlgebraicGeometry.IsOpenImmersion.of_openCover_sourceproof · cited by 1
- AlgebraicGeometry.Scheme.exists_hom_isAffine_of_isZariskiLocalAtSourceproof · cited by 1
- AlgebraicGeometry.isField_stalk_of_closure_mem_irreducibleComponentsproof · cited by 1