A trace for bimodule categories
2016 (English)In: Applied Categorical Structures, ISSN 0927-2852, E-ISSN 1572-9095Article in journal (Refereed) Epub ahead of print
We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued tracefor 1-morphisms in the tricategory of finite tensor categories. It is defined by a universalproperty that is a categorification of Hochschild homology of bimodules over an algebra.We present several equivalent realizations of this 2-functor and show that it has a coherent cyclic invariance.Our results have applications to categories associated to circles in three-dimensional topological field theories with defects. This is made explicit for the subclass of Dijkgraaf-Wittentopological field theories.
Place, publisher, year, edition, pages
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kau:diva-45611DOI: 10.1007/s10485-016-9425-3OAI: oai:DiVA.org:kau-45611DiVA: diva2:957077
FunderSwedish Research Council, 621-2013-4207