Weighted Tensor Products of Joyal Species, Graphs, and Charades

[摘要] 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.

[关键词] weighted derivation;Hurwitz series;monoidal category;Joyal species;convolution;Rota–Baxter operator