Theorems · Theorem · algebraic geometry
AlgebraicGeometry.HasAffineProperty.iff_of_openCover
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {Q : AlgebraicGeometry.AffineTargetMorphismProperty}
[AlgebraicGeometry.HasAffineProperty P Q] {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} (𝒰 : Y.OpenCover)
[inst : ∀ (i : 𝒰.I₀), AlgebraicGeometry.IsAffine (𝒰.X i)],
P f ↔ ∀ (i : 𝒰.toPreZeroHypercover.1), Q (AlgebraicGeometry.Scheme.Cover.pullbackHom 𝒰 f i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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 and proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xstatement and proof · 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.IsAffinestatement and proof · cited by 159
- AlgebraicGeometry.Scheme.Hom.opensRangeproof · cited by 113
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasAffineProperty.iff_of_isAffineproof · cited by 21