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Weighted Tensor Products of Joyal Species, Graphs, and Charades
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: weighted derivation; Hurwitz series; monoidal category; Joyal species; convolution; Rota–Baxter operator. 
@article{SIGMA_2016_12_a4,
     author = {Ross Street},
     title = {Weighted {Tensor} {Products} of {Joyal} {Species,} {Graphs,} and {Charades}},
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     volume = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a4/}
}
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Ross Street. Weighted Tensor Products of Joyal Species, Graphs, and Charades. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a4/

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