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december 2016 Coalgebras governing both weighted Hurwitz products and their pointwise transforms
Richard Garner, Ross Street
Bull. Belg. Math. Soc. Simon Stevin 23(5): 643-666 (december 2016). DOI: 10.36045/bbms/1483671619

Abstract

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.

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Richard Garner. Ross Street. "Coalgebras governing both weighted Hurwitz products and their pointwise transforms." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 643 - 666, december 2016. https://doi.org/10.36045/bbms/1483671619

Information

Published: december 2016
First available in Project Euclid: 6 January 2017

zbMATH: 1372.18007
MathSciNet: MR3593568
Digital Object Identifier: 10.36045/bbms/1483671619

Subjects:
Primary: 05A15 , 16T30 , 18A32 , 18D05 , 18D10 , 20H30

Keywords: convolution , Hurwitz series , Joyal species , monoidal category , Rota-Baxter operator , Weighted derivation

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 5 • december 2016
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