Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isoImage
{X Y : AlgebraicGeometry.Scheme} →
(f : X ⟶ Y) →
[inst : AlgebraicGeometry.IsOpenImmersion f] →
(U : X.Opens) → ↑U ≅ ↑((AlgebraicGeometry.Scheme.Hom.opensFunctor f).obj U)If f : X ⟶ Y is an open immersion, then for any U : X.Opens,
we have the isomorphism U ≅ f ''ᵁ U.
- Defined in
- Mathlib.AlgebraicGeometry.Restrict
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Isostatement · cited by 3,963
- 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
Cited by35
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialMap.compproof · cited by 15
- AlgebraicGeometry.Scheme.PartialIso.restrictSourceproof · cited by 10
- AlgebraicGeometry.Scheme.Hom.isoImage_hom_ιstatement · cited by 9
- AlgebraicGeometry.Scheme.PartialMap.comp_toPartialMapproof · cited by 3
- AlgebraicGeometry.Scheme.Opens.isoImage_ι_inv_ιstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.Opens.isoImage_ι_inv_ι_assocstatement and proof · cited by 3
- AlgebraicGeometry.morphismRestrictRestrictproof · cited by 2
- AlgebraicGeometry.Scheme.PartialIso.IsOver.restrictSourceproof · cited by 2
- AlgebraicGeometry.morphismRestrict_homOfLE_isoImage_ι_homstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.isoImage_hom_homOfLEstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.isoImage_hom_ι_assocstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.isoImage_inv_ιstatement · cited by 2