Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.image_le_image_iff
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.IsOpenImmersion f] (U U' : X.Opens),
(AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U ≤ (AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U' ↔ U ≤ U'- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · 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.PresheafedSpace.Hom.baseproof · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomproof · cited by 995
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.le_resLE_preimage_iffproof · cited by 6