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(WEAK) INCIDENCE BIALGEBRAS OF MONOIDAL CATEGORIES

Part of: Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  16 March 2020

ULRICH KRÄHMER  and
LUCIA ROTHERAY
ULRICH KRÄHMER
Affiliation:
Institut für Geometrie, Technische Universität Dresden, Dresden, Germany e-mails: ulrich.kraehmer@tu-dresden.de; lucia.rotheray@tu-dresden.de
LUCIA ROTHERAY
Affiliation:
Institut für Geometrie, Technische Universität Dresden, Dresden, Germany e-mails: ulrich.kraehmer@tu-dresden.de; lucia.rotheray@tu-dresden.de
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Abstract

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Incidence coalgebras of categories in the sense of Joni and Rota are studied, specifically cases where a monoidal product on the category turns these into (weak) bialgebras. The overlap with the theory of combinatorial Hopf algebras and that of Hopf quivers is discussed, and examples including trees, skew shapes, Milner’s bigraphs and crossed modules are considered.

MSC classification

Primary: 16T10: Bialgebras
Secondary: 16T05: Hopf algebras and their applications
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 1 , January 2021 , pp. 139 - 157
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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