Weighted tensor products of joyal species, graphs, and charades

Ross Street

doi:10.3842/SIGMA.2016.005

Weighted tensor products of joyal species, graphs, and charades

Ross Street^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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.

Original language	English
Article number	005
Pages (from-to)	1-20
Number of pages	20
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	12
DOIs	https://doi.org/10.3842/SIGMA.2016.005
Publication status	Published - 17 Jan 2016

Keywords

weighted derivation
Hurwitz series
monoidal category
Joyal species
convolution
Rota-Baxter operator

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10.3842/SIGMA.2016.005

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AB - 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.

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KW - Hurwitz series

KW - monoidal category

KW - Joyal species

KW - convolution

KW - Rota-Baxter operator

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ER -

Weighted tensor products of joyal species, graphs, and charades

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Structural homotopy theory: a category-theoretic study

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Weighted tensor products of joyal species, graphs, and charades

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Keywords

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Structural homotopy theory: a category-theoretic study

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