Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsZariskiLocalAtSource.of_openCover

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtSource P]
  {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} (𝒰 : X.OpenCover),
  (∀ (i : 𝒰.I₀), P (CategoryTheory.CategoryStruct.comp (𝒰.f i) f)) → P f

Defined in: Mathlib.AlgebraicGeometry.Morphisms.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsZariskiLocalAtSource

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Cites24

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 and proof · cited by 17,999
CategoryTheory.Iso.invproof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
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.Opens.toSchemeproof · cited by 433

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_openCoverproof · cited by 13
AlgebraicGeometry.HasRingHomProperty.isLocal_ringHomProperty_of_isZariskiLocalAtSource_of_isZariskiLocalAtTargetproof · cited by 1