symmetric monoidal (∞,1)-category of spectra
With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
The concept of a bimodule category is a categorification of that of bimodule, hence the two-sided version of the notion of a module category.
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.
Justin Greenough, Monoidal 2-structure of Bimodule Categories, Journal of Algebra 324 8 (2010) 1818-1859 [arXiv:0911.4979, doi:10.1016/j.jalgebra.2010.06.018]
Chris Douglas, Chris Schommer-Pries, Noah Snyder, Dualizable tensor categories, Memoirs of the American Mathematical Society (2020) [arXiv:1312.7188, ams:memo-268-1308]
Last revised on July 10, 2025 at 08:45:34. See the history of this page for a list of all contributions to it.