ΓObjEquivSections_naturality_symm

English

The global sections functor is isomorphic to Coyoneda of the terminal constant sheaf; i.e., a Yoneda-type representation of Γ.

Русский

Глобальные секции изоморфныCoyoneda-константного шейфа; т.е. представление типа Якцена Гондея.

LaTeX

$$$\Gamma J (Type max u v) \cong \mathrm{Coyoneda}.(op((\text{constantSheaf } J (Type max u v)).\mathrm{obj} X))$$$

Lean4

theorem ΓObjEquivSections_naturality_symm [HasWeakSheafify J (Type w)] [HasGlobalSectionsFunctor J (Type w)]
    {F G : Sheaf J (Type w)} (f : F ⟶ G) (x : F.val.sections) :
    (ΓObjEquivSections J G).symm ((Functor.sectionsFunctor _).map f.val x) =
      (Γ J _).map f ((ΓObjEquivSections J F).symm x) :=
  congr_fun (ΓHomEquiv_naturality_right (F.val.sectionsEquivHom _ x) f) _

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