Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isClosedImmersion_iff
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y),
AlgebraicGeometry.IsClosedImmersion f ↔ AlgebraicGeometry.SurjectiveOnStalks f ∧ Topology.IsClosedEmbedding ⇑f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsClosedImmersion.iff_isPreimmersionproof · cited by 1
- AlgebraicGeometry.IsClosedImmersion.eq_infproof · cited by 0