Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.IsClosedImmersion
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes X ⟶ Y is a closed immersion if the underlying
topological map is a closed embedding and the induced stalk maps are surjective.
- Cited by
- 49 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 by55
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.isClosedEmbeddingstatement · cited by 5
- AlgebraicGeometry.IsClosedImmersion.liftstatement and proof · cited by 5
- AlgebraicGeometry.IsClosedImmersion.lift_facstatement and proof · cited by 4
- AlgebraicGeometry.IsClosedImmersion.of_isPreimmersionstatement · cited by 4
- AlgebraicGeometry.IsClosedImmersion.of_compstatement and proof · cited by 3
- AlgebraicGeometry.isClosed_singleton_iff_isClosedImmersionstatement and proof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.isSeparated_iffstatement and proof · cited by 2
- AlgebraicGeometry.isClosedImmersion_iffstatement and proof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.iff_isFinite_and_monostatement and proof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.isIso_iff_ker_eq_botstatement and proof · cited by 2
- AlgebraicGeometry.IsClosedImmersion.isIso_of_ker_eqstatement and proof · cited by 2