Theorems · Theorem · algebraic geometry
RingHom.surjectiveOnStalks_iff_of_isLocalHom
∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {f : R →+* S} [IsLocalRing S] [IsLocalHom f],
f.SurjectiveOnStalks ↔ Function.Surjective ⇑f- Defined in
- Mathlib.RingTheory.SurjectiveOnStalks
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- one_mulproof · cited by 2,841
- Units.valproof · cited by 1,966
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
- IsUnit.unitproof · cited by 252
- IsLocalHomstatement and proof · cited by 100
- IsUnit.mul_val_invproof · cited by 29
- RingHom.SurjectiveOnStalksstatement and proof · cited by 26
- RingHom.surjectiveOnStalks_of_surjectiveproof · cited by 7
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