Weighted Tensor Products of Joyal Species, Graphs, and Charades

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.

References in corpus (2)

• Hopf monoidal comonads
• Monads and distributive laws for Rota-Baxter and differential algebras

Cited by in corpus (2)

• Classification of operator extensions, monad liftings and distributive laws for differential algebras and Rota-Baxter algebras
• Real sets