Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine

∀ {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 X]
  [AlgebraicGeometry.IsAffine Y], P f ↔ Q (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appTop f))

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

9 results in Mathlib

Foundations

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

Assumes

AlgebraicGeometry.HasRingHomPropertyAlgebraicGeometry.IsAffineAlgebraicGeometry.IsAffine