Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.image_mono
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f] {U V : X.Opens},
U ≤ V → (AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U ≤ (AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj V- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Scheme.Hom.opensFunctorstatement · cited by 204
Cited by24
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Opens.ι_image_leproof · cited by 6
- AlgebraicGeometry.IsAffineOpen.exists_basicOpen_leproof · cited by 5
- AlgebraicGeometry.Scheme.Hom.resLE_appLEproof · cited by 5
- AlgebraicGeometry.Scheme.Opens.ι_appLEproof · cited by 3
- AlgebraicGeometry.Scheme.Hom.isoImage_hom_homOfLEstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Modules.restrictAppIso_inv_mapstatement · cited by 2
- AlgebraicGeometry.Scheme.PartialMap.comp_equiv_of_equiv_rightproof · cited by 2
- AlgebraicGeometry.Scheme.Modules.map_restrictAppIso_homstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.appLE_appIso_invstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.isoImage_inv_homOfLEstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isoImage_inv_homOfLE_assocstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Modules.restrictAppIso_smul_Specproof · cited by 1