Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads
Gabriella B\"ohm

TL;DR
This paper develops a functorial framework linking Hopf polyads, Hopf categories, and Hopf group monoids as Hopf monads within a monoidal bicategory setting, unifying various structures in a categorical context.
Contribution
It introduces a functorial construction associating a monoidal bicategory to any monoidal bicategory, connecting different Hopf structures as Hopf monads in this framework.
Findings
Hopf polyads are Hopf monads in Span|Cat
Hopf group monoids are Hopf monads in Span|V
Hopf categories are Hopf monads in Span|V
Abstract
We associate, in a functorial way, a monoidal bicategory to any monoidal bicategory . Two examples of this construction are of particular interest: Hopf polyads (due to Brugui\`eres) can be seen as Hopf monads in while Hopf group monoids in a braided monoidal category (in the spirit of Turaev and Zunino), and Hopf categories over (by Batista, Caenepeel and Vercruysse) both turn out to be Hopf monads in . Hopf group monoids and Hopf categories are Hopf monads on a distinguished type of monoidales fitting the framework studied recently by B\"ohm and Lack. These examples are related by a monoidal pseudofunctor .
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
