Theorems · Theorem · algebraic geometry

RingHom.IsStableUnderBaseChange.pullback_fst_appTop

∀ (P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop),
  (RingHom.IsStableUnderBaseChange fun {R S} [CommRing R] [CommRing S] => P) →
    (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => P) →
      ∀ {X Y S : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsAffine X] [AlgebraicGeometry.IsAffine Y]
        [AlgebraicGeometry.IsAffine S] (f : X ⟶ S) (g : Y ⟶ S),
        P (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appTop g)) →
          P (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appTop (CategoryTheory.Limits.pullback.fst f g)))

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

2 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.IsAffineAlgebraicGeometry.IsAffineAlgebraicGeometry.IsAffine