isSeparatedFor_top — Mathlib

English

For any P, every presheaf is a sheaf for the maximal sieve ⊤ on X; i.e., isSheafFor_top_sieve.

Русский

Любой предшкеп есть sheafFor для максимального сита ⊤ на X.

LaTeX

$$IsSheafFor_top_sieve (P) : IsSheafFor P ((⊤ : Sieve X) : Presieve X)$$

Lean4

theorem isSeparatedFor_top (P : Cᵒᵖ ⥤ Type w) : IsSeparatedFor P (⊤ : Presieve X) := fun x t₁ t₂ h₁ h₂ =>
  by
  have q₁ := h₁ (𝟙 X) (by tauto)
  have q₂ := h₂ (𝟙 X) (by tauto)
  simp only [op_id, FunctorToTypes.map_id_apply] at q₁ q₂
  rw [q₁, q₂]

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