Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIso_iff_isOpenImmersion_and_epi_base
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y),
CategoryTheory.IsIso f ↔ AlgebraicGeometry.IsOpenImmersion f ∧ CategoryTheory.Epi f.base- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- 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
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement and proof · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomstatement and proof · cited by 995
- AlgebraicGeometry.Scheme.Hom.toLRSHom'statement and proof · cited by 895
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isIso_iff_isOpenImmersion_and_surjectiveproof · cited by 2
- AlgebraicGeometry.isIso_of_isOpenImmersion_of_opensRange_eq_topproof · cited by 2
- AlgebraicGeometry.isIso_iff_isIso_stalkMapproof · cited by 0