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Eilenberg-Watts calculus for finite categories and a bimodule Radford S4 theorem
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).ORCID iD: 0000-0003-4081-6234
Universität Wien, Austria.
Universität Hamburg, Germany.
2019 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850Article in journal (Refereed) Epub ahead of print
Abstract [en]

We obtain Morita invariant versions of Eilenberg-Watts type the-orems, relating Deligne products of finite linear categories to categories of leftexact as well as of right exact functors. This makes it possible to switch be-tween different functor categories as well as Deligne products, which is oftenvery convenient. For instance, we can show that applying the equivalence fromleft exact to right exact functors to the identity functor, regarded as a left exactfunctor, gives a Nakayama functor. The equivalences of categories we exhibitare compatible with the structure of module categories over finite tensor cat-egories. This leads to a generalization of Radford’sS4-theorem to bimodulecategories. We also explain the relation of our construction to relative Serrefunctors on module categories that are constructed via inner Hom functors.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2019.
National Category
Physical Sciences
Research subject
Mathematics; Physics
Identifiers
URN: urn:nbn:se:kau:diva-74944DOI: 10.1090/tran/7838OAI: oai:DiVA.org:kau-74944DiVA, id: diva2:1356358
Funder
Swedish Research Council, 621-2013-4207Available from: 2019-10-01 Created: 2019-10-01 Last updated: 2019-10-17Bibliographically approved

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Fuchs, Jürgen

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