Geodesic
(WEAK) INCIDENCE BIALGEBRAS OF MONOIDAL CATEGORIES
Glasgow mathematical journal, Tome 63 (2021) no. 1, pp. 139-157

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DOI

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. 
KRÄHMER, ULRICH; ROTHERAY, LUCIA. (WEAK) INCIDENCE BIALGEBRAS OF MONOIDAL CATEGORIES. Glasgow mathematical journal, Tome 63 (2021) no. 1, pp. 139-157. doi: 10.1017/S0017089520000075
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     title = {(WEAK) {INCIDENCE} {BIALGEBRAS} {OF} {MONOIDAL} {CATEGORIES}},
     journal = {Glasgow mathematical journal},
     pages = {139--157},
     year = {2021},
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     doi = {10.1017/S0017089520000075},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000075/}
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