Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.appLE

∀ (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),
  P f →
    ∀ (U : ↑Y.affineOpens) (V : ↑X.affineOpens) (e : ↑V ≤ (TopologicalSpace.Opens.map f.base).obj ↑U),
      Q (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appLE f (↑U) (↑V) e))

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

2 results in Mathlib

Foundations

Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.HasRingHomProperty