AddCommMonCat.equivalence.counitIso =
  CategoryTheory.Iso.refl
    ({ obj := fun X => AddCommMonCat.of (Additive ↑X),
          map := fun {X Y} f => AddCommMonCat.ofHom (MonoidHom.toAdditive (CommMonCat.Hom.hom f)),
          map_id := AddCommMonCat.equivalence._proof_3, map_comp := @AddCommMonCat.equivalence._proof_4 }.comp
      { obj := fun X => CommMonCat.of (Multiplicative ↑X),
        map := fun {X Y} f => CommMonCat.ofHom (AddMonoidHom.toMultiplicative (AddCommMonCat.Hom.hom f)),
        map_id := AddCommMonCat.equivalence._proof_1, map_comp := @AddCommMonCat.equivalence._proof_2 })