sheafificationHomEquiv — Mathlib

English

The forgetful functor from presheaf of modules to presheaf of rings preserves the monoidal structure.

Русский

Функтор забывания от прешефов модулей к прешефам колец сохраняет моноидальную структуру.

LaTeX

$$$\\mathrm{forget} \\circ \\mathrm{Monoidal} = \\mathrm{Monoidal} \\circ \\mathrm{forget}$$$

Lean4

/-- The bijection between types of morphisms which is part of the adjunction
`sheafificationAdjunction`. -/
noncomputable def sheafificationHomEquiv {P : PresheafOfModules.{v} R₀} {F : SheafOfModules.{v} R} :
    ((sheafification α).obj P ⟶ F) ≃ (P ⟶ (restrictScalars α).obj ((SheafOfModules.forget _).obj F)) := by
  apply sheafifyHomEquiv

Похожие утверждения