Theorems · Theorem · algebraic geometry
AlgebraicGeometry.HasAffineProperty.of_isPullback
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} {Q : AlgebraicGeometry.AffineTargetMorphismProperty}
[AlgebraicGeometry.HasAffineProperty P Q] {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y}
{UX UY : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsAffine UY] {iY : UY ⟶ Y}
[AlgebraicGeometry.IsOpenImmersion iY] {iX : UX ⟶ X} {f' : UX ⟶ UY}, CategoryTheory.IsPullback iX f' f iY → P f → Q f'- Cited by
- 3 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- CategoryTheory.IsPullbackstatement and proof · cited by 320
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
- AlgebraicGeometry.AffineTargetMorphismPropertystatement and proof · cited by 31
- AlgebraicGeometry.HasAffinePropertystatement and proof · cited by 30
- AlgebraicGeometry.HasAffineProperty.eq_targetAffineLocallyproof · cited by 10
- AlgebraicGeometry.of_targetAffineLocally_of_isPullbackproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.HasAffineProperty.isStableUnderBaseChangeproof · cited by 3
- AlgebraicGeometry.HasAffineProperty.diagonal_of_diagonal_of_isPullbackproof · cited by 1
- AlgebraicGeometry.HasAffineProperty.restrictproof · cited by 1