Eilenberg-Watts calculus for finite categories and a bimodule Radford $S^4$ theorem
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- by Jürgen Fuchs, Gregor Schaumann and Christoph Schweigert PDF
- Trans. Amer. Math. Soc. 373 (2020), 1-40
Abstract:
We obtain Morita invariant versions of Eilenberg-Watts type theorems, relating Deligne products of finite linear categories to categories of left exact as well as of right exact functors. This makes it possible to switch between different functor categories as well as Deligne products, which is often very convenient. For instance, we can show that applying the equivalence from left exact to right exact functors to the identity functor, regarded as a left exact functor, gives a Nakayama functor. The equivalences of categories we exhibit are compatible with the structure of module categories over finite tensor categories. This leads to a generalization of Radford’s $S^4$-theorem to bimodule categories. We also explain the relation of our construction to relative Serre functors on module categories that are constructed via inner Hom functors.References
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Additional Information
- Jürgen Fuchs
- Affiliation: Teoretisk fysik, Karlstads Universitet, Universitetsgatan 21, S–65188 Karlstad, Sweden; Fachbereich Mathematik, Universität Hamburg, Bereich Algebra und Zahlentheorie, Bundesstraße 55, D–20146 Hamburg, Germany
- MR Author ID: 209391
- ORCID: 0000-0003-4081-6234
- Gregor Schaumann
- Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A–1090 Wien, Austria
- MR Author ID: 976594
- Christoph Schweigert
- Affiliation: Fachbereich Mathematik, Universität Hamburg, Bereich Algebra und Zahlentheorie, Bundesstraße 55, D–20146 Hamburg, Germany
- MR Author ID: 328535
- ORCID: 0000-0003-1342-6230
- Received by editor(s): January 19, 2017
- Received by editor(s) in revised form: December 22, 2018
- Published electronically: October 1, 2019
- Additional Notes: The first author was supported by VR under project No. 621-2013-4207.
The second author was supported by Nils Carqueville’s project P 27513-N27 of the Austrian Science Fund.
The third author was partially supported by the Collaborative Research Centre 676 “Particles, Strings and the Early Universe - The Structure of Matter and Space-Time” and by the RTG 1670 “Mathematics Inspired by String Theory and Quantum Field Theory”. - © Copyright 2019 Jürgen Fuchs, Gregor Schaumann, and Christoph Schweigert
- Journal: Trans. Amer. Math. Soc. 373 (2020), 1-40
- MSC (2010): Primary 16T05; Secondary 18D10, 16Gxx
- DOI: https://doi.org/10.1090/tran/7838
- MathSciNet review: 4042867