Theorems · Theorem · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.pullback_snd_isIso_of_range_subset
∀ {X Y Z : AlgebraicGeometry.LocallyRingedSpace} (f : X ⟶ Z) (g : Y ⟶ Z)
[H : AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion f],
Set.range ⇑(CategoryTheory.ConcreteCategory.hom g.base) ⊆ Set.range ⇑(CategoryTheory.ConcreteCategory.hom f.base) →
CategoryTheory.IsIso (CategoryTheory.Limits.pullback.snd f g)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Set.rangestatement and proof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- 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
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.liftproof · cited by 7
- AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.lift_rangeproof · cited by 0