Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.isMultiplicative

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme}
  {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}
  [AlgebraicGeometry.HasRingHomProperty P Q],
  (RingHom.StableUnderComposition fun {R S} [CommRing R] [CommRing S] => Q) →
    (RingHom.ContainsIdentities fun {R S} [CommRing R] [CommRing S] => Q) → P.IsMultiplicative

Defined in: Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties
Cited by: 0 results in Mathlib
Foundations: Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.HasRingHomProperty

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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
RingHomstatement and proof · cited by 10,189
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
CategoryTheory.MorphismProperty.IsMultiplicativestatement · cited by 332
AlgebraicGeometry.HasRingHomPropertystatement and proof · cited by 38
RingHom.StableUnderCompositionstatement and proof · cited by 26
RingHom.ContainsIdentitiesstatement and proof · cited by 12

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