∀ {X Y : CommMonCat}
  (f : (CategoryTheory.forget₂ CommMonCat MonCat).obj X ⟶ (CategoryTheory.forget₂ CommMonCat MonCat).obj Y),
  (CategoryTheory.forget₂ CommMonCat MonCat).map (CommMonCat.ofHom (MonCat.Hom.hom f)) = f