Oplax Hopf Algebras

We introduce the notion of an (op)lax Hopf monoid in any monoidal 2-category, generalizing that of a Hopf monoid in a 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 2-category Span|V described in [B\"oh17]. Finally, we introduce Frobenius V-categories as the Frobenius objects in the same monoidal 2-category.