Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsZariskiLocalAtTarget.of_isPullback
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtTarget P]
{X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {UX UY : AlgebraicGeometry.Scheme} {iY : UY ⟶ Y}
[AlgebraicGeometry.IsOpenImmersion iY] {iX : UX ⟶ X} {f' : UX ⟶ UY}, CategoryTheory.IsPullback iX f' f iY → P f → P f'- Cited by
- 6 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Scheme.affineCoverproof · cited by 61
- AlgebraicGeometry.IsZariskiLocalAtTargetstatement and proof · cited by 36
- AlgebraicGeometry.Scheme.Cover.addproof · cited by 4
- CategoryTheory.MorphismProperty.IsLocalAtTarget.of_isPullbackproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtTarget.iff_of_openCoverproof · cited by 18
- AlgebraicGeometry.IsZariskiLocalAtTarget.restrictproof · cited by 8
- AlgebraicGeometry.isClosedMap_iff_specializingMapproof · cited by 1
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlongproof · cited by 1
- AlgebraicGeometry.isOpenMap_of_generalizingMapproof · cited by 0
- AlgebraicGeometry.HasRingHomProperty.stableUnderCompositionproof · cited by 0