Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasAffineProperty.affineAnd_isStableUnderBaseChange

∀ {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}
  {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme},
  AlgebraicGeometry.HasAffineProperty P (AlgebraicGeometry.affineAnd fun {R S} [CommRing R] [CommRing S] => Q) →
    (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => Q) →
      (RingHom.IsStableUnderBaseChange fun {R S} [CommRing R] [CommRing S] => Q) → P.IsStableUnderBaseChange

If P is a morphism property affine locally defined by affineAnd Q, P is stable under base change if Q is.

Defined in

Mathlib.AlgebraicGeometry.Morphisms.AffineAnd

Cited by

0 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound