2016/11/16 by Gabriella Böhm, Böhm, Gabriella
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.1611.05157
openalex publication_date 2016/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We associate, in a functorial way, a monoidal bicategory Span| \mathcal V to any monoidal bicategory \mathcal V. Two examples of this construction are of particular interest: Hopf polyads (due to Bruguières) can be seen as Hopf monads in Span| Cat while Hopf group monoids in a braided monoidal category V (in the spirit of Turaev and Zunino), and Hopf categories over V (by Batista, Caenepeel and Vercruysse) both turn out to be Hopf monads in Span| V. Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fitting the framework studied recently by Böhm and Lack. These examples are related by a monoidal pseudofunctor V→ Cat.