of_comp — Mathlib

English

Surjectivity on stalks is characterized by stalk maps being surjective at every point.

Русский

Суръективность по пикам определяется тем, что отображения стел на каждой точке сюръективны.

LaTeX

$$eq_stalkwise : SurjectiveOnStalks f = stalkwise (Function.Surjective ·) f$$

Lean4

theorem of_comp [SurjectiveOnStalks (f ≫ g)] : SurjectiveOnStalks f :=
  by
  refine ⟨fun x ↦ ?_⟩
  have := (f ≫ g).stalkMap_surjective x
  rw [Scheme.stalkMap_comp] at this
  exact Function.Surjective.of_comp this

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