Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIntegral_of_isOpenImmersion
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsOpenImmersion f] [AlgebraicGeometry.IsIntegral Y]
[Nonempty ↥X], AlgebraicGeometry.IsIntegral X- Defined in
- Mathlib.AlgebraicGeometry.Properties
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- IsDomainproof · cited by 2,196
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensproof · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.presheafproof · cited by 1,104
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isIntegral_of_isAffine_of_isDomainproof · cited by 0
- AlgebraicGeometry.IsIntegral.of_isIsoproof · cited by 0