whiskeringLeftEquivalence — Mathlib

Lean4

/-- The equivalence of categories `(W.localization ⥤ D) ≌ (W.FunctorsInverting D)`
induced by the composition with `W.Q : C ⥤ W.localization`. -/
def whiskeringLeftEquivalence : W.Localization ⥤ D ≌ W.FunctorsInverting D
    where
  functor := WhiskeringLeftEquivalence.functor W D
  inverse := WhiskeringLeftEquivalence.inverse W D
  unitIso := WhiskeringLeftEquivalence.unitIso W D
  counitIso := WhiskeringLeftEquivalence.counitIso W D
  functor_unitIso_comp
    F := by
    ext
    simp only [WhiskeringLeftEquivalence.unitIso_hom, eqToHom_app, eqToHom_refl,
      WhiskeringLeftEquivalence.counitIso_hom, eqToHom_map, eqToHom_trans]
    rfl

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