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Oplax Hopf Algebras

We introduce the notion of an oplax Hopf monoid in any braided monoidal bicategory, generalizing that of a Hopf monoid in a braided monoidal category in an appropriate way. We show that Hopf V-categories introduced in [BCV16] are a particular type of oplax Hopf monoids in the monoidal bicategory Span|V described in [Böh17]. Finally, we introduce Frobenius V-categories as the Frobenius objects in the same monoidal bicategory.