Theorems · Theorem · algebraic geometry

AlgebraicGeometry.affineAnd_isLocal

∀ {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => Q) →
    (RingHom.LocalizationAwayPreserves fun {R S} [CommRing R] [CommRing S] => Q) →
      (RingHom.OfLocalizationSpan fun {R S} [CommRing R] [CommRing S] => Q) →
        (AlgebraicGeometry.affineAnd fun {R S} [CommRing R] [CommRing S] => Q).IsLocal

affineAnd P is local if P is local on the (algebraic) source.

Defined in

Mathlib.AlgebraicGeometry.Morphisms.AffineAnd

Cited by

2 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound