Theorems · Definition · category theory

CommRingCat.Under.createsFiniteLimitsForget

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

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

Defined in

Mathlib.Algebra.Category.Ring.Under.Property

Cited by

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Foundations

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