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SIGMA 12 (2016), 005, 20 pages arXiv:1503.02783
https://doi.org/10.3842/SIGMA.2016.005
Weighted Tensor Products of Joyal Species, Graphs, and Charades
Ross Street
Centre of Australian Category Theory, Macquarie University, Australia
Received August 18, 2015, in final form January 14, 2016; Published online January 17, 2016
Abstract
Motivated by the weighted Hurwitz product on sequences in an algebra, we produce a family of monoidal structures on the category of Joyal species. We suggest a family of tensor products for charades. We begin by seeing weighted derivational algebras and weighted Rota-Baxter algebras as special monoids and special semigroups, respectively, for the same monoidal structure on the category of graphs in a monoidal additive category. Weighted derivations are lifted to the categorical level.
Key words:
weighted derivation; Hurwitz series; monoidal category; Joyal species; convolution; Rota-Baxter operator.
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