Theorems · Theorem · category theory

RingHom.HasStableEqualizers.preservesLimit_parallelPair_tensorProd

∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.HasStableEqualizers fun {R S} [CommRing R] [CommRing S] => P) →
    ∀ {R S : CommRingCat} [inst : Algebra ↑R ↑S] {A B : CategoryTheory.Under R} (f g : A ⟶ B),
      P (CommRingCat.Hom.hom A.hom) →
        P (CommRingCat.Hom.hom B.hom) →
          CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.parallelPair f g) (R.tensorProd S)

Defined in

Mathlib.Algebra.Category.Ring.Under.Property

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Algebra