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.