Theorems · Theorem · algebraic geometry

PrimeSpectrum.isQuotientMap_of_generalizingMap

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] {f : R →+* S},
  Function.Surjective (PrimeSpectrum.comap f) →
    GeneralizingMap (PrimeSpectrum.comap f) → Topology.IsQuotientMap (PrimeSpectrum.comap f)

If f : Spec S → Spec R is generalizing and surjective, the topology on Spec R is the quotient topology induced by f.

Defined in

Mathlib.RingTheory.Spectrum.Prime.Topology

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiring