Theorems · Theorem · commutative algebra

RingHom.locally_localizationPreserves

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

If P is preserved by localizations, then so is Locally P.

Defined in

Mathlib.RingTheory.RingHom.Locally

Cited by

0 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound