(Weak) incidence bialgebras of monoidal categories

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.

16 pages, 25 PNG figures

References in corpus (4)

• Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
• Hopf algebras, from basics to applications to renormalization
• Group Objects and Internal Categories
• Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals