Theorems · Theorem · algebraic geometry
PrimeSpectrum.localization_comap_isInducing
∀ {R : Type u} (S : Type v) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (M : Submonoid R)
[IsLocalization M S], Topology.IsInducing (PrimeSpectrum.comap (algebraMap R S))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Idealproof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsClosedproof · cited by 1,639
- Ideal.spanproof · cited by 948
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.localization_comap_isEmbeddingproof · cited by 2