Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.UniversallyClosed
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes f : X ⟶ Y is universally closed if the base change X ×[Y] Y' ⟶ Y'
along any morphism Y' ⟶ Y is (topologically) a closed map.
- Cited by
- 24 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 by28
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.isClosedMapstatement and proof · cited by 6
- AlgebraicGeometry.UniversallyClosed.universally_isClosedMapstatement and proof · cited by 4
- AlgebraicGeometry.universallyClosed_eqstatement · cited by 2
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomstatement and proof · cited by 2
- AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterionstatement · cited by 2
- AlgebraicGeometry.UniversallyClosed.of_comp_surjectivestatement and proof · cited by 2
- AlgebraicGeometry.isProper_eqstatement and proof · cited by 2
- AlgebraicGeometry.IsIntegralHom.eq_universallyClosed_inf_isAffineHomstatement · cited by 1
- AlgebraicGeometry.compactSpace_of_universallyClosedstatement and proof · cited by 1
- AlgebraicGeometry.universallyClosed_eq_universallySpecializingstatement and proof · cited by 1
- AlgebraicGeometry.isField_of_universallyClosedstatement and proof · cited by 1
- AlgebraicGeometry.universallyClosed_iffstatement and proof · cited by 1