Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.respects_isOpenImmersion

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme}
  {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}
  [AlgebraicGeometry.HasRingHomProperty P Q],
  (RingHom.StableUnderCompositionWithLocalizationAwaySource fun {R S} [CommRing R] [CommRing S] => Q) →
    P.Respects AlgebraicGeometry.IsOpenImmersion

Any property of scheme morphisms induced by a property of ring homomorphisms is stable under composition with open immersions.

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

1 results in Mathlib

Foundations

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

Assumes

AlgebraicGeometry.HasRingHomProperty