Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsZariskiLocalAtSource.iff_of_iSup_eq_top

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtSource P]
  {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {ι : Sort u_1} (U : ι → X.Opens),
  iSup U = ⊤ → (P f ↔ ∀ (i : ι), P (CategoryTheory.CategoryStruct.comp (U i).ι f))

Defined in: Mathlib.AlgebraicGeometry.Morphisms.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsZariskiLocalAtSource

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

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
Top.topstatement and proof · cited by 9,680
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
iSupstatement and proof · cited by 2,415
CommRingCatstatement · cited by 2,333
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734

Cited by3

Results whose statement or proof uses this declaration.

AlgebraicGeometry.HasRingHomProperty.of_compproof · cited by 3
AlgebraicGeometry.IsZariskiLocalAtSource.iff_exists_resLEproof · cited by 2
AlgebraicGeometry.HasRingHomProperty.of_stalkMapproof · cited by 1