Theorems · Theorem · commutative algebra

RingHom.locally_stableUnderCompositionWithLocalizationAwaySource

∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.StableUnderCompositionWithLocalizationAwaySource fun {R S} [CommRing R] [CommRing S] => P) →
    RingHom.StableUnderCompositionWithLocalizationAwaySource fun {R S} [CommRing R] [CommRing S] =>
      RingHom.Locally fun {R S} [CommRing R] [CommRing S] => P

If P is stable under composition with localization away maps on the left, then so is Locally P.

Defined in: Mathlib.RingTheory.RingHom.Locally
Cited by: 3 results in Mathlib
Foundations: Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebraproof · cited by 11,388
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Top.topproof · cited by 9,680
Algebra.algebraMapproof · cited by 4,706
Ideal.spanproof · cited by 948
RingHom.compproof · cited by 899
IsLocalization.Awayproof · cited by 218
Localization.Awayproof · cited by 162
RingHom.Locallystatement and proof · cited by 28
RingHom.comp_assocproof · cited by 27

Cited by3

Results whose statement or proof uses this declaration.

AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallyproof · cited by 3
RingHom.locally_propertyIsLocalproof · cited by 1
RingHom.locally_StableUnderCompositionWithLocalizationAwaySourceproof · cited by 0