Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.IsImmersion
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes f : X ⟶ Y is an immersion if
1. the underlying map of topological spaces is an embedding
2. the range of the map is locally closed
3. the induced morphisms of stalks are all surjective.
- Cited by
- 17 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 by23
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.coborderRangestatement and proof · cited by 8
- AlgebraicGeometry.Scheme.Hom.liftCoborderstatement and proof · cited by 6
- AlgebraicGeometry.Scheme.Hom.liftCoborder_ιstatement and proof · cited by 6
- AlgebraicGeometry.IsImmersion.of_compstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.liftCoborder_preimagestatement and proof · cited by 2
- AlgebraicGeometry.liftCoborder_appstatement and proof · cited by 1
- AlgebraicGeometry.isImmersion_iffstatement and proof · cited by 1
- AlgebraicGeometry.isIso_of_comp_eq_sigmaSpecstatement and proof · cited by 1
- AlgebraicGeometry.IsLocallyArtinian.of_isImmersionstatement and proof · cited by 1
- AlgebraicGeometry.IsImmersion.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.IsImmersion.isLocallyClosed_rangestatement and proof · cited by 1
- AlgebraicGeometry.IsImmersion.recOnstatement and proof · cited by 0