sheaf_for_finestTopology — Mathlib

English

The functor yoneda.obj X is a sheaf for the canonical topology on C.

Русский

Функтор yoneda.obj X является sheaf для канонической топологии на C.

LaTeX

$$$\\mathrm{Presieve.IsSheaf}(\\text{canonicalTopology } C)\, (\\mathrm{yoneda.obj}\\ X)$$$

Lean4

/-- Check that if `P ∈ Ps`, then `P` is indeed a sheaf for the finest topology on `Ps`. -/
theorem sheaf_for_finestTopology (Ps : Set (Cᵒᵖ ⥤ Type v)) (h : P ∈ Ps) : Presieve.IsSheaf (finestTopology Ps) P :=
  fun X S hS => by simpa using hS _ ⟨⟨_, _, ⟨_, h, rfl⟩, rfl⟩, rfl⟩ _ (𝟙 _)

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