instIsZariskiLocalAtTargetStalkwiseBijectiveCoeRingHom

English

Instance: IsZariskiLocalAtTarget for stalkwise bijective ring homomorphisms.

Русский

Экземпляр: IsZariskiLocalAtTarget для локально-бийевых отображений колец.

LaTeX

$$$ IsZariskiLocalAtTarget (stalkwise (\lambda f. Bijective (RingHom.instFunLike.coe f))) $$$

Lean4

instance : IsZariskiLocalAtTarget (stalkwise (fun f ↦ Function.Bijective f)) :=
  by
  apply stalkwiseIsZariskiLocalAtTarget_of_respectsIso
  rw [RingHom.toMorphismProperty_respectsIso_iff]
  convert (inferInstanceAs (MorphismProperty.isomorphisms CommRingCat).RespectsIso)
  ext
  exact (ConcreteCategory.isIso_iff_bijective _).symm

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