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I have two questions concerning the coproduct of weak bialgebras. First, I would like to know if there is a proof of the existence of the coproduct in the category of weak bialgebras?

Second, (assuming the answer to the first question is yes) do we actually know how to construct it? For example, something similar to this construction (Pareigis, p.57) for bialgebras?

Thanks, Steve

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