Products of coalgebras

@inproceedings{Gumm2001ProductsOC,
  title={Products of coalgebras},
  author={H. Peter Gumm and Tobias Schr{\"o}der},
  year={2001}
}
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 A × B and the largest bisimulation ∼A,B betweenA andB and find an example of two finite coalgebras whose product is infinite. 

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