Theorems · Theorem · algebraic geometry
AlgebraicGeometry.SheafedSpace.IsOpenImmersion.to_iso
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : AlgebraicGeometry.SheafedSpace C} (f : X ⟶ Y)
[H : AlgebraicGeometry.SheafedSpace.IsOpenImmersion f] [h' : CategoryTheory.Epi f.hom.base], CategoryTheory.IsIso fAn open immersion is an iso if the underlying continuous map is epi.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.mapproof · cited by 8,698
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- TopCatstatement · cited by 1,889
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement and proof · cited by 1,135
- CategoryTheory.InducedCategory.Hom.homstatement and proof · cited by 850
- CategoryTheory.Epistatement and proof · cited by 688
- AlgebraicGeometry.PresheafedSpacestatement · cited by 260
- AlgebraicGeometry.SheafedSpacestatement and proof · cited by 142
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.to_isoproof · cited by 1