Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasAffineProperty.coprodDesc_affineAnd

∀ {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) →
      (∀ {R S T : Type u} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T] (f : R →+* S) (g : R →+* T),
          Q f → Q g → Q (f.prod g)) →
        ∀ {U V X : AlgebraicGeometry.Scheme} (f : U ⟶ X) (g : V ⟶ X),
          P f → P g → P (CategoryTheory.Limits.coprod.desc f g)

Defined in

Mathlib.AlgebraicGeometry.Morphisms.AffineAnd

Cited by

0 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound