Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.UniversallyInjective
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes f : X ⟶ Y is universally injective if the base change X ×[Y] Y' ⟶ Y'
along any morphism Y' ⟶ Y is injective (on points).
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.injectivestatement and proof · cited by 4
- AlgebraicGeometry.universallyInjective_eq_diagonalstatement and proof · cited by 2
- AlgebraicGeometry.UniversallyInjective.universally_injectivestatement and proof · cited by 2
- AlgebraicGeometry.universallyInjective_iffstatement and proof · cited by 1
- AlgebraicGeometry.UniversallyInjective.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.UniversallyInjective.iff_diagonalstatement · cited by 1
- AlgebraicGeometry.universallyInjective_eqstatement · cited by 1
- AlgebraicGeometry.UniversallyInjective.recOnstatement and proof · cited by 0
- AlgebraicGeometry.tfae_universallyInjectivestatement and proof · cited by 0
- AlgebraicGeometry.UniversallyInjective.respectsIsostatement · cited by 0