Theorems · Definition · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict
{X Y : AlgebraicGeometry.LocallyRingedSpace} →
(f : X ⟶ Y) → [H : AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion f] → X ≅ Y.restrict ⋯An open immersion is isomorphic to the induced open subscheme on its image.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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.Isostatement · cited by 3,963
- 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.PresheafedSpace.Hom.basestatement · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomproof · cited by 995
- CategoryTheory.InducedCategory.Hom.homstatement · cited by 850
- AlgebraicGeometry.PresheafedSpacestatement · cited by 260
- AlgebraicGeometry.LocallyRingedSpacestatement and proof · cited by 205
- AlgebraicGeometry.SheafedSpacestatement · cited by 142
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrictstatement and proof · cited by 2
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrictstatement and proof · cited by 1
- AlgebraicGeometry.IsOpenImmersion.isoRestrictproof · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_hom_ofRestrict_assocstatement and proof · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.isoRestrict_inv_ofRestrict_assocstatement and proof · cited by 0