A unified treatment of commuting tensor products of categories, operads, symmetric multicategories and their bimodules
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914163038617600 |
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| author | Gambino, Nicola Garner, Richard Vasilakopoulou, Christina |
| author_facet | Gambino, Nicola Garner, Richard Vasilakopoulou, Christina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A unified treatment of commuting tensor products of categories, operads, symmetric multicategories and their bimodules Gambino, Nicola Garner, Richard Vasilakopoulou, Christina Category Theory 18N10, 18N15, 18M80, 18M05 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. |
| title | A unified treatment of commuting tensor products of categories, operads, symmetric multicategories and their bimodules |
| topic | Category Theory 18N10, 18N15, 18M80, 18M05 |
| url | https://arxiv.org/abs/2511.14402 |