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A trace for bimodule categories
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för ingenjörsvetenskap och fysik (from 2013).ORCID-id: 0000-0003-4081-6234
Max-Planck-Institut für Mathematik, Bonn.
Hamburg University.
2017 (engelsk)Inngår i: Applied Categorical Structures, ISSN 0927-2852, E-ISSN 1572-9095, Vol. 25, nr 2, s. 227-268Artikkel i tidsskrift (Fagfellevurdert) Published
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.

sted, utgiver, år, opplag, sider
2017. Vol. 25, nr 2, s. 227-268
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:kau:diva-45611DOI: 10.1007/s10485-016-9425-3ISI: 000399877600004OAI: oai:DiVA.org:kau-45611DiVA, id: diva2:957077
Forskningsfinansiär
Swedish Research Council, 621-2013-4207Tilgjengelig fra: 2016-08-31 Laget: 2016-08-31 Sist oppdatert: 2019-06-17bibliografisk kontrollert

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