Theorems · Theorem · category theory

RingHom.HasFiniteProducts.preservesFiniteProducts_pushout

∀ {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => Q) →
    (RingHom.HasFiniteProducts fun {R S} [CommRing R] [CommRing S] => Q) →
      ∀ [inst : (RingHom.toMorphismProperty fun {R S} [CommRing R] [CommRing S] => Q).IsStableUnderCobaseChange]
        {R S : CommRingCat} (f : R ⟶ S),
        CategoryTheory.Limits.PreservesFiniteProducts
          (CategoryTheory.MorphismProperty.Under.pushout
            (RingHom.toMorphismProperty fun {R S} [CommRing R] [CommRing S] => Q) ⊤ f)

Defined in

Mathlib.Algebra.Category.Ring.Under.Property

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.MorphismProperty.IsStableUnderCobaseChange