### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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