Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Cover.ulift

{X : AlgebraicGeometry.Scheme} →
  {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} →
    AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X →
      AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X

Any v-cover 𝒰 induces a u-cover indexed by the points of X.

Defined in: Mathlib.AlgebraicGeometry.Cover.MorphismProperty
Cited by: 9 results in Mathlib
Foundations: Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

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

Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopCat.carrierproof · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
CategoryTheory.PreZeroHypercover.Xproof · cited by 649
CategoryTheory.PreZeroHypercover.fproof · cited by 542
CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
AlgebraicGeometry.Scheme.precoveragestatement and proof · cited by 336
AlgebraicGeometry.Scheme.Coverstatement and proof · cited by 88

Cited by11

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Cover.hom_extproof · cited by 18
AlgebraicGeometry.Scheme.Cover.ι_glueMorphismsproof · cited by 12
AlgebraicGeometry.Scheme.Cover.glueMorphismsproof · cited by 10
AlgebraicGeometry.IsZariskiLocalAtTarget.mk'proof · cited by 3
AlgebraicGeometry.IsZariskiLocalAtSource.mk'proof · cited by 2
AlgebraicGeometry.Scheme.mem_grothendieckTopology_iffproof · cited by 2
AlgebraicGeometry.Scheme.Cover.qculiftproof · cited by 0
AlgebraicGeometry.HasAffineProperty.isZariskiLocalAtSourceproof · cited by 0
AlgebraicGeometry.Scheme.Cover.ulift_I₀statement and proof · cited by 0
AlgebraicGeometry.Scheme.Cover.ulift_Xstatement and proof · cited by 0
AlgebraicGeometry.Scheme.Cover.ulift_fstatement and proof · cited by 0