Products of coalgebras

Abstract. We prove that the category of F-coalgebras is complete, that is products and equalizers exist, provided that the type functor F is bounded or preserves mono sources. This generalizes and simplifies a result of Worrell ([Wor98]). We also describe the relationship between the product $ \Cal A \times \Cal B $ and the largest bisimulation $ \sim_{\Cal A,\Cal B} $ between $ \Cal A $ and $ \Cal B $ and find an example of two finite coalgebras whose product is infinite.