Theorems · Theorem · algebraic geometry
AlgebraicGeometry.SmoothOfRelativeDimension.smooth
∀ (n : ℕ) {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.SmoothOfRelativeDimension n f],
AlgebraicGeometry.Smooth fIf f is smooth of any relative dimension, it is smooth.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- CategoryTheory.Functor.objproof · cited by 19,642
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensproof · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.Hom.baseproof · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomproof · cited by 995
- AlgebraicGeometry.Scheme.Hom.toLRSHom'proof · cited by 895
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsSmoothOfRelativeDimension.isSmoothproof · cited by 0