of_isSheaf_yoneda_obj — Mathlib

English

If P is representable, then P is a Presieve.IsSheaf for canonical topology.

Русский

Если P представим, то P — Presieve.IsSheaf для канонической топологии.

LaTeX

$$$P\\text{ representable} \\Rightarrow \\mathrm{IsSheaf}(\\text{canonicalTopology}, P)$$$

Lean4

/-- If every functor `yoneda.obj X` is a `J`-sheaf, then `J` is subcanonical. -/
theorem of_isSheaf_yoneda_obj (J : GrothendieckTopology C) (h : ∀ X, Presieve.IsSheaf J (yoneda.obj X)) : Subcanonical J
    where le_canonical := le_finestTopology _ _ (by rintro P ⟨X, rfl⟩; apply h)

Похожие утверждения