Theorems · Definition · category theory

RingHom.HasEqualizers.createsLimitsWalkingParallelPair

{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.HasEqualizers fun {R S} [CommRing R] [CommRing S] => Q) →
      (R : CommRingCat) →
        CategoryTheory.CreatesLimitsOfShape CategoryTheory.Limits.WalkingParallelPair
          (CategoryTheory.MorphismProperty.Under.forget
            (RingHom.toMorphismProperty fun {R S} [CommRing R] [CommRing S] => Q) ⊤ R)

If Q is stable under equalizers, the inclusion from the subcategory of Under R defined by Q creates equalizers.

Defined in

Mathlib.Algebra.Category.Ring.Under.Property

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound