Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover

∀ {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]
  (𝒰 : X.OpenCover) [∀ (i : 𝒰.I₀), AlgebraicGeometry.IsAffine (𝒰.X i)],
  P f ↔
    ∀ (i : 𝒰.I₀),
      Q (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appTop (CategoryTheory.CategoryStruct.comp (𝒰.f i) f)))

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

1 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.HasRingHomPropertyAlgebraicGeometry.IsAffineAlgebraicGeometry.IsAffine