Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f],
(AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj ⊤ = AlgebraicGeometry.Scheme.Hom.opensRange f- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 17 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 · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- 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
Cited by17
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.exists_map_preimage_le_map_preimageproof · cited by 3
- AlgebraicGeometry.Scheme.PartialMap.comp_toPartialMapproof · cited by 3
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
- AlgebraicGeometry.exists_app_map_eq_zero_of_isLimitproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.of_source_openCoverproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimageproof · cited by 2
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- AlgebraicGeometry.IsZariskiLocalAtTarget.of_range_subset_iSupproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.opensRange_comp_of_isIsoproof · cited by 1
- AlgebraicGeometry.spread_out_unique_of_isGermInjectiveproof · cited by 1
- AlgebraicGeometry.HasRingHomProperty.of_iSup_eq_topproof · cited by 1