Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.of_comp

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme}
  {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}
  [AlgebraicGeometry.HasRingHomProperty P Q],
  (∀ {R S T : Type u} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T] (f : R →+* S) (g : S →+* T),
      Q (g.comp f) → Q g) →
    ∀ {X Y Z : AlgebraicGeometry.Scheme} {f : X ⟶ Y} {g : Y ⟶ Z}, P (CategoryTheory.CategoryStruct.comp f g) → P f

Defined in

Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties

Cited by

3 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.HasRingHomProperty