Theorems · Theorem · commutative algebra

RingHom.locally_isStableUnderBaseChange

∀ {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.IsStableUnderBaseChange fun {R S} [CommRing R] [CommRing S] => P) →
      RingHom.IsStableUnderBaseChange fun {R S} [CommRing R] [CommRing S] =>
        RingHom.Locally fun {R S} [CommRing R] [CommRing S] => P

If P is stable under base change, then so is Locally P.

Defined in: Mathlib.RingTheory.RingHom.Locally
Cited by: 1 results in Mathlib
Foundations: Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites35

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

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Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.smoothOfRelativeDimension_isStableUnderBaseChangeproof · cited by 1