fac — Mathlib

English

There is a canonical equivalence between the objects of C and the objects of its localization W.Localization.

Русский

Существует каноническое эквивалентность объектов C и объектов локализации W.Localization.

LaTeX

$$$\text{objEquiv}: C \simeq W.Localization$$$

Lean4

@[simp]
theorem fac : W.Q ⋙ lift G hG = G :=
  Functor.ext (fun _ => rfl)
    (by
      intro X Y f
      simp only [Functor.comp_map, eqToHom_refl, comp_id, id_comp]
      dsimp [MorphismProperty.Q, Quot.liftOn, Quotient.functor]
      rw [composePath_toPath])

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