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A trace for bimodule categories
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.ORCID iD: 0000-0003-4081-6234
Max-Planck-Institut für Mathematik, Bonn.
Hamburg University.
2016 (English)In: Applied Categorical Structures, ISSN 0927-2852, E-ISSN 1572-9095Article in journal (Refereed) Epub ahead of print
Abstract [en]

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.

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URN: urn:nbn:se:kau:diva-45611DOI: 10.1007/s10485-016-9425-3OAI: diva2:957077
Swedish Research Council, 621-2013-4207
Available from: 2016-08-31 Created: 2016-08-31 Last updated: 2016-12-27Bibliographically approved

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Fuchs, Jürgen
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