Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.iff_of_iSup_eq_top

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme}
  {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}
  [AlgebraicGeometry.HasRingHomProperty P Q] {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} [AlgebraicGeometry.IsAffine Y]
  {ι : Type u_1} (U : ι → ↑X.affineOpens),
  ⨆ i, ↑(U i) = ⊤ → (P f ↔ ∀ (i : ι), Q (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appLE f ⊤ ↑(U i) ⋯)))

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

0 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.HasRingHomPropertyAlgebraicGeometry.IsAffine