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Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads
Theory and applications of categories, Tome 32 (2017), pp. 1229-1257

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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.

Publié le :
Classification : 18D05, 18D10, 18D35, 16T05
Keywords: monoidal bicategory, monoidale, Hopf monad, Hopf polyad, Hopf category, Hopf group algebra 
Gabriella Böhm. Hopf polyads, Hopf categories and Hopf group monoids viewed as Hopf monads. Theory and applications of categories, Tome 32 (2017), pp. 1229-1257. http://geodesic.mathdoc.fr/item/TAC_2017_32_a36/
@article{TAC_2017_32_a36,
     author = {Gabriella B\"ohm},
     title = {Hopf polyads, {Hopf} categories and {Hopf} group monoids viewed as {Hopf} monads},
     journal = {Theory and applications of categories},
     pages = {1229--1257},
     year = {2017},
     volume = {32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a36/}
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