Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads

Gabriella Böhm

We associate, in a functorial way, a monoidal bicategory Span|V to any monoidal bicategory V. Two examples of this construction are of particular interest: Hopf polyads of Bruguieres can be seen as Hopf monads in Span|Cat while Hopf group monoids in the spirit of Zunino and Turaev in a braided monoidal category V, and Hopf categories of Batista-Caenepeel-Vercruysse over V 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 of Bohm-Lack. These examples are related by a monoidal pseudofunctor V -> Cat.

Keywords: monoidal bicategory, monoidale, Hopf monad, Hopf polyad, Hopf category, Hopf group algebra

2010 MSC: 18D05, 18D10, 18D35, 16T05

Theory and Applications of Categories, Vol. 32, 2017, No. 37, pp 1229-1257.

Published 2017-09-18.


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