Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsClosedImmersion.isIso_iff_ker_eq_bot
∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} [AlgebraicGeometry.IsClosedImmersion f],
CategoryTheory.IsIso f ↔ AlgebraicGeometry.Scheme.Hom.ker f = ⊥- Cited by
- 2 results in Mathlib
- Foundations
- Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Bot.botstatement and proof · cited by 4,720
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- AlgebraicGeometry.Scheme.IdealSheafDatastatement · cited by 192
- AlgebraicGeometry.Scheme.Hom.kerstatement and proof · cited by 51
- AlgebraicGeometry.IsClosedImmersionstatement and proof · cited by 49
- AlgebraicGeometry.Scheme.Hom.imageιproof · cited by 13
- AlgebraicGeometry.Scheme.Hom.toImage_imageιproof · cited by 11
- AlgebraicGeometry.Scheme.Hom.ker_eq_bot_of_isIsoproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isIso_of_isClosedImmersion_of_surjectiveproof · cited by 1
- AlgebraicGeometry.IsClosedImmersion.isIso_of_injective_of_isAffineproof · cited by 0