Theorems · Definition · commutative algebra
RingHom.StableUnderCompositionWithLocalizationAway
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) → PropA property P of ring homs satisfies RingHom.StableUnderCompositionWithLocalizationAway
if whenever P holds for f it also holds for the composition with
localization maps on the left and on the right.
- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- RingHom.StableUnderCompositionWithLocalizationAwaySourceproof · cited by 6
- RingHom.StableUnderCompositionWithLocalizationAwayTargetproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- RingHom.StableUnderComposition.stableUnderCompositionWithLocalizationAwaystatement · cited by 7
- RingHom.StableUnderCompositionWithLocalizationAway.respectsIsostatement and proof · cited by 1
- RingHom.locally_propertyIsLocalstatement and proof · cited by 1
- RingHom.isStandardSmooth_stableUnderCompositionWithLocalizationAwaystatement · cited by 1
- RingHom.isStandardSmoothOfRelativeDimension_stableUnderCompositionWithLocalizationAwaystatement · cited by 0
- AlgebraicGeometry.HasRingHomProperty.locally_of_iffstatement and proof · cited by 0