Theorems · Theorem · algebraic geometry
RingHom.surjectiveOnStalks_of_surjective
∀ {R : Type u_1} [inst : CommRing R] {S : Type u_2} [inst_1 : CommRing S] {f : R →+* S},
Function.Surjective ⇑f → f.SurjectiveOnStalks- Defined in
- Mathlib.RingTheory.SurjectiveOnStalks
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Top.topproof · cited by 9,680
- Idealproof · cited by 4,748
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- map_oneproof · cited by 861
- RingHom.SurjectiveOnStalksstatement · cited by 26
- RingHom.surjectiveOnStalks_iff_forall_idealproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.surjectiveOnStalks_residueFieldproof · cited by 3
- RingEquiv.surjectiveOnStalksproof · cited by 2
- RingHom.SurjectiveOnStalks.baseChange'proof · cited by 2
- Algebra.weaklyQuasiFiniteAt_iffproof · cited by 2
- Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAtproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_restrictScalarsproof · cited by 1
- RingHom.surjectiveOnStalks_iff_of_isLocalHomproof · cited by 0