Geodesic
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 
@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},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a36/}
}
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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/