yonedaEquiv_symm_naturality_right

English

Similar left variant on the right: for F, F' and f: F → F', x ∈ F(X), one has J.yonedaEquiv.symm x ≫ f = J.yonedaEquiv.symm (f.val.app ⟨X⟩ x).

Русский

Аналогично справа: для F, F' и f: F → F', x ∈ F(X) выполняется J.yonedaEquiv.symm x ≫ f = J.yonedaEquiv.symm (f.x.app ⟨X⟩ x).

LaTeX

$$$J.yonedaEquiv.symm x \;\; \;\; f = J.yonedaEquiv.symm (f.app ⟨X⟩ x)$$$

Lean4

theorem yonedaEquiv_symm_naturality_right (X : C) {F F' : Sheaf J (Type v)} (f : F ⟶ F') (x : F.val.obj ⟨X⟩) :
    J.yonedaEquiv.symm x ≫ f = J.yonedaEquiv.symm (f.val.app ⟨X⟩ x) :=
  by
  apply J.yonedaEquiv.injective
  simp [yonedaEquiv_comp]

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