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Keywords:
Hopf algebras; Frobenius algebras; bialgebras; monoidal bicategories; enriched categories
Hopf algebras; Frobenius algebras; bialgebras; monoidal bicategories; enriched categories
Summary:
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 $\mathcal{V}$-categories introduced in [4] are a particular type of oplax Hopf monoids in the monoidal bicategory ${\bf Span}|\mathcal{V}$ described in [5]. Finally, we introduce Frobenius $\mathcal{V}$-categories as the Frobenius objects in the same monoidal bicategory.
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