Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_openCover
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtSource P]
{X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} (𝒰 : X.OpenCover),
P f ↔ ∀ (i : 𝒰.I₀), P (CategoryTheory.CategoryStruct.comp (𝒰.f i) f)- Cited by
- 13 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.PreZeroHypercover.I₀statement and proof · 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
- AlgebraicGeometry.IsZariskiLocalAtSourcestatement and proof · cited by 37
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.IsLocalIso.le_of_isZariskiLocalAtSourceproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_finite_preimage_singletonproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.isStableUnderBaseChangeproof · cited by 1
- AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singletonproof · cited by 1
- AlgebraicGeometry.Scheme.exists_hom_isAffine_of_isZariskiLocalAtSourceproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.descendsAlongproof · cited by 1
- AlgebraicGeometry.universally_isZariskiLocalAtSourceproof · cited by 0
- AlgebraicGeometry.Smooth.of_smooth_fiberToSpecResidueFieldproof · cited by 0
- AlgebraicGeometry.IsZariskiLocalAtSource.sigmaDescproof · cited by 0
- AlgebraicGeometry.isOpenMap_of_generalizingMapproof · cited by 0