Braided monoidal categories of coalgebras

Let V be a braided monoidal category. Given a braided monoidal endofunctor F on V , it is proved that F -coalgebras form a braided monoidal category, denoted as V F . Particularly, if the category V admits coproducts and if F is a fully faithful symmetric monoidal endofunctor, then it is proved that V F is symmetric monoidal closed whenever V is symmetric monoidal closed.