∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₁, u₂} D]
  {G : CategoryTheory.Functor D C} {F : CategoryTheory.Functor C D} (adj : F ⊣ G) (A : adj.toMonad.Algebra) (B : D)
  [inst_2 : CategoryTheory.Limits.HasCoequalizer (F.map A.a) (adj.counit.app (F.obj A.A))]
  (a : A ⟶ (CategoryTheory.Monad.comparison adj).obj B),
  (CategoryTheory.Monad.MonadicityInternal.comparisonLeftAdjointHomEquiv adj A B).symm a =
    (CategoryTheory.Limits.Cofork.IsColimit.homIso
          (CategoryTheory.Limits.colimit.isColimit
            (CategoryTheory.Limits.parallelPair (F.map A.a) (adj.counit.app (F.obj A.A))))
          B).symm
      ⟨(adj.homEquiv A.A B).symm a.f, ⋯⟩