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(WEAK) INCIDENCE BIALGEBRAS OF MONOIDAL CATEGORIES

Published online by Cambridge University Press:  16 March 2020

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

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.

Type
Research Article
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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