5 papers
Generalized Yetter-Drinfeld modules, the center of bi-actegories and groupoid-crossed braided bicategories
Ryan Aziz, Joost Vercruysse
We study the notion of the -center of a -biactegory (or bimodule category) , relative to an op-monoidal fun…
Dualities for universal (co)acting Hopf monoids
Ana Agore, Alexey Gordienko, Joost Vercruysse
In general, universal (co)measuring (co)monoids and universal (co)acting bi/Hopf monoids, which prove to be a useful tool in the classification of quantum symmetries, do not always…
Lifting of locally initial objects and universal (co)acting Hopf algebras
Ana Agore, Alexey Gordienko, Joost Vercruysse
The universal (co)acting bi/Hopf algebras introduced by Yu. I. Manin, M. Sweedler and D. Tambara, the universal Hopf algebra of a given (co)module structure, as well as the univers…
Globalization and the biactegory of partial modules
Eliezer Batista, William Hautekiet, Joost Vercruysse
We show that the category of partial modules over a Hopf algebra is a biactegory (a bimodule category) over the category of global -modules. The corresponding enrichment of…
Free and co-free constructions for Hopf categories
Paul GroÃkopf, Joost Vercruysse
We show that under mild conditions on the monoidal base category , the category of Hopf -categories is locally presentable and deduce the exis…