Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 23, Number 5 (2016), 643-666.
Coalgebras governing both weighted Hurwitz products and their pointwise transforms
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.
Bull. Belg. Math. Soc. Simon Stevin, Volume 23, Number 5 (2016), 643-666.
First available in Project Euclid: 6 January 2017
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Primary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 18A32: Factorization of morphisms, substructures, quotient structures, congruences, amalgams 18D05: Double categories, 2-categories, bicategories and generalizations 20H30: Other matrix groups over finite fields 16T30: Connections with combinatorics
Garner, Richard; Street, Ross. Coalgebras governing both weighted Hurwitz products and their pointwise transforms. Bull. Belg. Math. Soc. Simon Stevin 23 (2016), no. 5, 643--666. https://projecteuclid.org/euclid.bbms/1483671619