Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.image_of_isOpenImmersion
∀ {X Y : AlgebraicGeometry.Scheme} {U : X.Opens},
AlgebraicGeometry.IsAffineOpen U →
∀ (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f],
AlgebraicGeometry.IsAffineOpen ((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U)- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.objstatement · cited by 19,642
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- 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
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- AlgebraicGeometry.IsAffineOpenstatement and proof · cited by 222
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.HasRingHomProperty.comp_of_isOpenImmersionproof · cited by 4
- AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersionstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.ideal_comap_of_isOpenImmersionstatement and proof · cited by 1
- AlgebraicGeometry.sourceAffineLocally_respectsIsoproof · cited by 1
- AlgebraicGeometry.Scheme.ker_morphismRestrict_idealstatement and proof · cited by 0
- AlgebraicGeometry.isLocallyNoetherian_of_isOpenImmersionproof · cited by 0
- AlgebraicGeometry.IsImmersion.isPullback_toImage_liftCoborderproof · cited by 0