Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf
∀ {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) =
AlgebraicGeometry.Scheme.Hom.opensRange f ⊓ U- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- SetLike.coeproof · cited by 8,199
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- 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
Cited by15
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.le_resLE_preimage_iffproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.image_preimage_leproof · cited by 5
- AlgebraicGeometry.Scheme.opensRange_homOfLEproof · cited by 3
- AlgebraicGeometry.Scheme.image_basicOpenproof · cited by 3
- AlgebraicGeometry.Scheme.Hom.appLE_appIso_invstatement and proof · cited by 2
- AlgebraicGeometry.IsZariskiLocalAtTarget.of_range_subset_iSupproof · cited by 1
- AlgebraicGeometry.Scheme.Modules.restrictAppIso_smul_Specproof · cited by 1
- AlgebraicGeometry.isAffineHom_diagonal_iffproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assocstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isPullback_resLEproof · cited by 1