equivYoneda' — Mathlib

English

Similar to equivYoneda but for a sheaf S; gives a canonical isomorphism to Yoneda on S(*) object.

Русский

Аналогично equivYoneda, но в случае шарфа S; каноническое изоморфирование с Yoneda на S(*)

LaTeX

$$$ S \\cong yoneda'.obj (S. obj { unop := PUnit }) $$$

Lean4

/-- Given a sheaf `S`, construct an isomorphism `S ≅ [-, S(*)]`. -/
@[simps]
noncomputable def equivYoneda' (S : Sheaf typesGrothendieckTopology (Type u)) : S ≅ yoneda'.obj (S.1.obj (op PUnit))
    where
  hom := ⟨(equivYoneda S.1 S.2).hom⟩
  inv := ⟨(equivYoneda S.1 S.2).inv⟩
  hom_inv_id := by ext1; apply (equivYoneda S.1 S.2).hom_inv_id
  inv_hom_id := by ext1; apply (equivYoneda S.1 S.2).inv_hom_id

Похожие утверждения