dsimp [Functor.comp, Functor.id]
α : Type u
inst✝ : Category α
⊢ Prefunctor.obj mapF.toPrefunctor singletonF ⋙ joinF = 𝟭 (List α)
α : Type u
inst✝ : Category α
⊢ Functor.mk
      { obj :=
          fun X ↦
            Prefunctor.obj joinF.toPrefunctor
              (Prefunctor.obj (Prefunctor.obj mapF.toPrefunctor singletonF).toPrefunctor X),
        map :=
          fun {X Y} f ↦
            Prefunctor.map joinF.toPrefunctor
              (Prefunctor.map (Prefunctor.obj mapF.toPrefunctor singletonF).toPrefunctor f) } =
    Functor.mk { obj := fun X ↦ X, map := fun {X Y} f ↦ f }