Theorems · Theorem · commutative algebra

PrimeSpectrum.mapPiLocalization_naturality

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S),
  (PrimeSpectrum.mapPiLocalization f).comp ↑(PrimeSpectrum.toPiLocalization R) =
    (PrimeSpectrum.toPiLocalization S).comp f

Defined in: Mathlib.RingTheory.Spectrum.Maximal.Localization
Cited by: 1 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring CommSemiring

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

DFunLike.coeproof · cited by 62,936
Algebraproof · cited by 11,388
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AlgHomstatement · cited by 3,236
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map_oneproof · cited by 861
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IsLocalizationproof · cited by 636
PrimeSpectrumstatement and proof · cited by 625
AlgHom.toRingHomstatement · cited by 490

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PrimeSpectrum.finite_of_toPiLocalization_surjectiveproof · cited by 1