2025/11/18 by Gambino, Nicola, Garner, Richard, Vasilakopoulou, Christina
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · doi:10.48550/arxiv.2511.14402
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.