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Weak (Hopf) bialgebras are described as (Hopf) bimonoids in appropriate duoidal (also known as 2-monoidal) categories. This interpretation is used to define a category wba of weak bialgebras over a given field. As an application, the “free vector space” functor from the category of small categories with finitely many objects to wba is shown to possess a right adjoint, given by taking (certain) group-like...