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arXiv · 2511.14402

A unified treatment of commuting tensor products of categories, operads, symmetric multicategories and their bimodules

Nicola Gambino·Richard Garner·Christina Vasilakopoulou
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Abstract

We provide a unified treatment of several commuting tensor products considered in the literature, including the tensor product of enriched categories and the Boardman-Vogt tensor product of operads and symmetric multicategories, subsuming work of Elmendorf and Mandell. We then show how a commuting tensor product extends to bimodules, generalising results of Dwyer and Hess. In particular, we construct a double category of symmetric multicategories, symmetric multifunctors and bimodules and show that it admits a symmetric oplax monoidal structure. These applications are obtained as instances of a general construction of commuting tensor products on double categories of monads, monad morphisms and bimodules.

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Nicola Gambino, Richard Garner, Christina Vasilakopoulou. 2025-11-18. A unified treatment of commuting tensor products of categories, operads, symmetric multicategories and their bimodules. https://arxiv.org/abs/2511.14402

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