equivOfIso — Mathlib

English

Two isomorphic sheaves have equivalent families of generating sections via the isomorphism.

Русский

Две изоморфные шары модуля дают эквивалентные множества порождающих секций через изоморфизм.

LaTeX

$$equivOfIso : M \cong N \Rightarrow M.GeneratingSections \simeq N.GeneratingSections$$

Lean4

/-- Two isomorphic sheaves of modules have equivalent families of generating sections. -/
def equivOfIso (e : M ≅ N) : M.GeneratingSections ≃ N.GeneratingSections
    where
  toFun σ := σ.ofEpi e.hom
  invFun σ := σ.ofEpi e.inv
  left_inv
    σ := by
    dsimp
    simp only [← opEpi_comp, e.hom_inv_id, opEpi_id]
  right_inv
    σ := by
    dsimp
    simp only [← opEpi_comp, e.inv_hom_id, opEpi_id]

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