isSheaf_of_isRepresentable — Mathlib

English

A representable presheaf is a J-sheaf if J is subcanonical.

Русский

Representable-прешепаф является J-шейфом, если J=subcanonical.

LaTeX

$$$P\\text{ representable} \\Rightarrow \\mathrm{Presieve.IsSheaf}(J,P)$$$

Lean4

/-- A representable functor is a sheaf for the canonical topology. -/
theorem isSheaf_of_isRepresentable (P : Cᵒᵖ ⥤ Type v) [P.IsRepresentable] : Presieve.IsSheaf (canonicalTopology C) P :=
  Presieve.isSheaf_iso (canonicalTopology C) P.reprW (isSheaf_yoneda_obj _)

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