Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.opensRange_of_isIso
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : CategoryTheory.IsIso f],
AlgebraicGeometry.Scheme.Hom.opensRange f = ⊤- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.IsIso
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Top.topstatement · cited by 9,680
- TopCat.carrierstatement · cited by 3,184
- 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
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
- AlgebraicGeometry.Scheme.Hom.opensRangestatement · cited by 113
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.opensRange_comp_of_isIsoproof · cited by 1
- AlgebraicGeometry.Scheme.exists_isAffine_of_isLimitproof · cited by 1
- AlgebraicGeometry.Scheme.IsLocallyDirected.glueDataι_naturalityproof · cited by 1
- AlgebraicGeometry.Scheme.IsLocallyDirected.V_selfproof · cited by 0