Theorems · Theorem · category theory

RingHom.HasFiniteProducts.hasFiniteProducts

∀ {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) →
      ∀ (R : CommRingCat),
        CategoryTheory.Limits.HasFiniteProducts
          ((RingHom.toMorphismProperty fun {R S} [CommRing R] [CommRing S] => Q).Under ⊤ R)

Defined in: Mathlib.Algebra.Category.Ring.Under.Property
Cited by: 1 results in Mathlib
Foundations: Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CommRingstatement and proof · cited by 17,173
CategoryTheory.Functorproof · cited by 16,252
RingHomstatement and proof · cited by 10,189
Top.topstatement and proof · cited by 9,680
CategoryTheory.Functor.idstatement · cited by 3,333
CategoryTheory.Discretestatement and proof · cited by 2,447
CommRingCatstatement and proof · cited by 2,333
CategoryTheory.MorphismPropertystatement · cited by 2,179
CategoryTheory.Functor.fromPUnitstatement · cited by 769
CategoryTheory.Limits.HasFiniteProductsstatement · cited by 142
RingHom.RespectsIsostatement and proof · cited by 78
CategoryTheory.MorphismProperty.Understatement and proof · cited by 43

Cited by1

Results whose statement or proof uses this declaration.

CommRingCat.Under.hasFiniteLimitsproof · cited by 1