yonedaGluedToSheaf_app_toGlued — Mathlib

English

The glued-to-sheaf component at each i interacts compatibly with the toGlued maps, i.e., the i-th app of the glued-sheaf is the Yoneda equivalence of f_i.

Русский

Компонента глуэд-до-шииф в i-го элемента: отображение i-го компонента равносильно yonedaEquiv(f_i).

LaTeX

$$$(\\yonedaGluedToSheaf\\;hf).\\text{val}.app {\\,unop := X\\}(toGlued\\;hf\\;i) = \\yonedaEquiv (f_i)$$$

Lean4

@[simp]
theorem yonedaGluedToSheaf_app_toGlued {i : ι} : (yonedaGluedToSheaf hf).val.app _ (toGlued hf i) = yonedaEquiv (f i) :=
  by rw [← yoneda_toGlued_yonedaGluedToSheaf hf i, yonedaEquiv_comp, yonedaEquiv_yoneda_map]

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