Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight
{X Y Z : AlgebraicGeometry.Scheme} →
X.OpenCover → Y.OpenCover → (f : X ⟶ Z) → (g : Y ⟶ Z) → (CategoryTheory.Limits.pullback f g).OpenCoverGiven an open cover { Xᵢ } of X and an open cover { Yⱼ } of Y, then
X ×[Z] Y is covered by Xᵢ ×[Z] Yⱼ.
- Defined in
- Mathlib.AlgebraicGeometry.Pullbacks
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Equiv.symmproof · cited by 3,681
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Limits.pullbackstatement and proof · cited by 864
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
- CategoryTheory.Limits.pullback.mapproof · cited by 156
Cited by9
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Pullback.diagonalCoverproof · cited by 6
- AlgebraicGeometry.HasAffineProperty.diagonal_of_openCoverproof · cited by 2
- AlgebraicGeometry.Scheme.Pullback.diagonalCover_mapstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Pullback.diagonalRestrictIsoDiagonalstatement · cited by 1
- AlgebraicGeometry.SurjectiveOnStalks.isEmbedding_pullbackproof · cited by 0
- AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_I₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_Xstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRight_fstatement and proof · cited by 0