bimodule category

The concept of a *bimodule category* is a categorification of that of bimodule. Where a bimodule is an abelian group acted on by two rings, so a bimodule category is a suitable category suitably acted on by two monoidal categories, hence a 2-sided *module category*.

For instance

- Chris Douglas, Chris Schommer-Pries, Noah Snyder,
*Dualizable tensor categories*(arXiv:1312.7188)