Theorems · Definition · algebraic geometry
AlgebraicGeometry.IsOpenImmersion.isoRestrict
{X Z : AlgebraicGeometry.Scheme} → (f : X ⟶ Z) → [H : AlgebraicGeometry.IsOpenImmersion f] → X ≅ Z.restrict ⋯An open immersion induces an isomorphism from the domain onto the image
- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- 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.PresheafedSpace.Hom.basestatement · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomstatement · cited by 995
- AlgebraicGeometry.Scheme.Hom.toLRSHom'statement · cited by 895
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
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