Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.image_preimage_le
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f] (U : Y.Opens),
(AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj ((TopologicalSpace.Opens.map f.base).obj U) ≤ U- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 105 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 · 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.basestatement · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomstatement · cited by 995
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.exists_basicOpen_leproof · cited by 5
- AlgebraicGeometry.Scheme.Hom.isoImage_preimage_hom_homOfLEstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.id_compproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isoImage_preimage_hom_homOfLE_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Modules.restrictAdjunction_unit_app_appstatement · cited by 0