Coalgebras governing both weighted Hurwitz products and their pointwise transforms

Richard Garner*, Ross Street

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    We give further insights into the weighted Hurwitz product and the weighted tensor product of Joyal species. Our first group of results relate the Hurwitz product to the pointwise product, including the interaction with Rota Baxter operators. Our second group of results explain the first in terms of convolution with suitable bialgebras, and show that these bialgebras are in fact obtained in a particularly straightforward way by freely generating from pointed coalgebras. Our third group of results extend this from linear algebra to two-dimensional linear algebra, deriving the existence of weighted Hurwitz monoidal structures on the category of species using convolution with freely generated bimonoidales. Our final group of results relate Hurwitz monoidal structures with equivalences of Dold-Kan type.

    Original languageEnglish
    Pages (from-to)643-666
    Number of pages24
    JournalBulletin of the Belgian Mathematical Society - Simon Stevin
    Issue number5
    Publication statusPublished - 2016
    EventInternational Conference on New Trends in Hopf Algebras and Tensor Categories - Brussels, Belgium
    Duration: 2 Jun 20155 Jun 2015


    • Weighted derivation
    • Hurwitz series
    • monoidal category
    • Joyal species
    • convolution
    • Rota-Baxter operator


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