isoSheafify_inv — Mathlib

English

The inverse of the isomorphism isoSheafify J hP is given by the sheafifyLift of the identity on P.

Русский

Обратное изоморфизмом ι является lift идентичности.

LaTeX

$$((isoSheafify J hP).inv) = \mathrm{sheafifyLift} J (\mathrm{Id} _) hP$$

Lean4

@[simp]
theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : (isoSheafify J hP).inv = sheafifyLift J (𝟙 _) hP :=
  by
  apply sheafifyLift_unique
  simp [Iso.comp_inv_eq]

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