Oplax Hopf Algebras
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 [B��h17]. Finally, we introduce Frobenius V-categories as the Frobenius objects in the same monoidal bicategory.
42 pages; numerous substantial changes and additions throughout the paper, to appear in `Higher Structures'
- Vrije Universiteit Brussel Belgium
- University of Patras Greece
- Université Libre de Bruxelles Belgium
Hopf algebras and their applications, Frobenius algebras, bialgebras, enriched categories, Mathematics - Category Theory, monoidal bicategories, Mathematics - Rings and Algebras, Théorie des ensembles et catégories, 2-categories, bicategories, double categories, Enriched categories (over closed or monoidal categories), Bialgebras, Hopf algebras, Rings and Algebras (math.RA), FOS: Mathematics, Monoidal categories, symmetric monoidal categories, Category Theory (math.CT)
Hopf algebras and their applications, Frobenius algebras, bialgebras, enriched categories, Mathematics - Category Theory, monoidal bicategories, Mathematics - Rings and Algebras, Théorie des ensembles et catégories, 2-categories, bicategories, double categories, Enriched categories (over closed or monoidal categories), Bialgebras, Hopf algebras, Rings and Algebras (math.RA), FOS: Mathematics, Monoidal categories, symmetric monoidal categories, Category Theory (math.CT)
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