Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_openCover
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtTarget P]
{X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} (𝒰 : Y.OpenCover),
P f ↔ ∀ (i : 𝒰.toPreZeroHypercover.1), P (AlgebraicGeometry.Scheme.Cover.pullbackHom 𝒰 f i)- Cited by
- 18 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.PreZeroHypercover.I₀statement · cited by 763
- CategoryTheory.PreZeroHypercover.Xstatement · cited by 649
- CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542
- AlgebraicGeometry.IsOpenImmersionstatement · cited by 476
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469
- AlgebraicGeometry.Scheme.precoveragestatement · cited by 336
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
- CategoryTheory.IsPullback.of_hasPullbackproof · cited by 70
- CategoryTheory.Precoverage.ZeroHypercover.pullback₁statement · cited by 64
Cited by18
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsFinite.iff_isIntegralHom_and_locallyOfFiniteTypeproof · cited by 2
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_finite_preimage_singletonproof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.iff_isFinite_and_monoproof · cited by 2
- AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singletonproof · cited by 1
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1
- AlgebraicGeometry.isClosedMap_iff_specializingMapproof · cited by 1
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlongproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_iff_surjectiveproof · cited by 0