Theorems · Theorem · commutative algebra
RingHom.Smooth.propertyIsLocal
RingHom.PropertyIsLocal fun {R S} [CommRing R] [CommRing S] => RingHom.SmoothSmoothness is a local property of ring homomorphisms.
- Defined in
- Mathlib.RingTheory.RingHom.Smooth
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement · cited by 17,173
- RingHom.Smoothstatement · cited by 30
- RingHom.PropertyIsLocalstatement · cited by 20
- RingHom.IsStableUnderBaseChange.localizationPreservesproof · cited by 11
- RingHom.LocalizationPreserves.awayproof · cited by 9
- RingHom.OfLocalizationSpanTarget.ofLocalizationSpanproof · cited by 7
- RingHom.Smooth.holdsForLocalizationAwayproof · cited by 2
- RingHom.Smooth.isStableUnderBaseChangeproof · cited by 2
- RingHom.Smooth.ofLocalizationSpanTargetproof · cited by 2
- RingHom.Smooth.stableUnderCompositionproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- RingHom.Etale.propertyIsLocalproof · cited by 3
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2
- RingHom.smooth_iff_locally_isStandardSmoothproof · cited by 1
- RingHom.Smooth.respectsIsoproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iffproof · cited by 0