toSheafify — Mathlib

English

There is a canonical morphism from a presheaf of modules to the underlying sheaf obtained by smul-compatible construction.

Русский

Существует канонический морфин от презаписи модулей к основанной шейфе через совместное построение скалярного умножения.

LaTeX

$$$\text{toSheafify}: M_{0} \to (\restrictScalars(\alpha).obj (\text{sheafify}(\alpha, \varphi)).val).$$$

Lean4

/-- The canonical morphism from a presheaf of modules to its associated sheaf. -/
noncomputable def toSheafify : M₀ ⟶ (restrictScalars α).obj (sheafify α φ).val :=
  homMk φ
    (fun X r₀ m₀ ↦ by
      simpa using (Sheafify.map_smul_eq α φ (α.app _ r₀) (φ.app _ m₀) (𝟙 _) r₀ (by simp) m₀ (by simp)).symm)

Похожие утверждения