Theorems · Theorem · algebraic geometry
IsLocalHom.of_comap_surjective
∀ {R : Type u} {S : Type v} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S),
Function.Surjective (PrimeSpectrum.comap f) → IsLocalHom f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Idealproof · cited by 4,748
- IsUnitproof · cited by 1,602
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.IsMaximalproof · cited by 452
- PrimeSpectrum.comapstatement and proof · cited by 199
- IsLocalHomstatement · cited by 100
- Ideal.IsPrime.ne_topproof · cited by 82
- Ideal.mem_comapproof · cited by 54
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