isSheafFor_top_sieve — Mathlib

English

The presheaf P is a sheaf for the maximal sieve on X, i.e., isSheafFor_top_sieve.

Русский

Предшкеп P является sheaf для максимального сита на X.

LaTeX

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

Lean4

/-- Every presheaf is a sheaf for the maximal sieve.

[Elephant] C2.1.5(ii)
-/
theorem isSheafFor_top_sieve (P : Cᵒᵖ ⥤ Type w) : IsSheafFor P ((⊤ : Sieve X) : Presieve X) :=
  by
  rw [← generate_of_singleton_isSplitEpi (𝟙 X)]
  rw [← isSheafFor_iff_generate]
  apply isSheafFor_singleton_iso

Похожие утверждения