Theorems · Theorem · commutative algebra

RingHom.locally_iff_of_localizationSpanTarget

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

If P is local on the target, then Locally P coincides with P.

Defined in

Mathlib.RingTheory.RingHom.Locally

Cited by

3 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRing