Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iff

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {S : AlgebraicGeometry.Scheme}
  [inst : P.IsStableUnderBaseChange] {X : CategoryTheory.Over S} (R : CategoryTheory.Sieve X)
  (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X.left)
  [inst_1 : AlgebraicGeometry.Scheme.Cover.Over S 𝒰],
  𝒰.toPresieveOver ≤ R.arrows ↔ CategoryTheory.Presieve.ofArrows 𝒰.X 𝒰.f ≤ ((CategoryTheory.Sieve.overEquiv X) R).arrows

Defined in: Mathlib.AlgebraicGeometry.Sites.Small
Cited by: 1 results in Mathlib
Foundations: Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.MorphismProperty.IsStableUnderBaseChange AlgebraicGeometry.Scheme.Cover.Over

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CategoryTheory.Sievestatement and proof · cited by 552
CategoryTheory.PreZeroHypercover.fstatement and proof · cited by 542
CategoryTheory.Over.leftstatement and proof · cited by 541
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverstatement and proof · cited by 469

Cited by1

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AlgebraicGeometry.Scheme.overGrothendieckTopology_eq_toGrothendieck_overPretopologyproof · cited by 1