∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F G : CategoryTheory.Functor C C} (adj : F ⊣ G)
  {X Y : CategoryTheory.Endofunctor.Coalgebra G} (f : X ⟶ Y),
  ((CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf adj).map f).f = f.f