Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Pullback.openCoverOfRight
{X Y Z : AlgebraicGeometry.Scheme} →
Y.OpenCover → (f : X ⟶ Z) → (g : Y ⟶ Z) → (CategoryTheory.Limits.pullback f g).OpenCoverGiven an open cover { Yᵢ } of Y, then X ×[Z] Y is covered by X ×[Z] Yᵢ.
- Defined in
- Mathlib.AlgebraicGeometry.Pullbacks
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.Iso.homproof · cited by 7,684
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Limits.pullbackstatement and proof · cited by 864
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.PreZeroHypercover.fproof · cited by 542
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- Equiv.reflproof · cited by 274
- AlgebraicGeometry.Scheme.OpenCoverstatement and proof · cited by 207
- CategoryTheory.Limits.pullback.mapproof · cited by 156
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Pullback.openCoverOfLeftRightproof · cited by 7
- AlgebraicGeometry.HasRingHomProperty.isStableUnderBaseChangeproof · cited by 1
- AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_fstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_I₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.Pullback.openCoverOfRight_Xstatement and proof · cited by 0