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Simple Transitive 2-Representations via (Co-)Algebra 1-Morphisms
Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Dept Matemat, P-1049001 Lisbon, Portugal;Univ Algarve, Dept Matemat, FCT, Campus Gambelas, P-8005139 Faro, Portugal.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-4633-6218
Univ East Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England.
Univ Bonn, Math Inst, Endenicher Allee 60,Room 1-003, D-53115 Bonn, Germany;Univ Zurich, Inst Math, Winterthurerstr 190,Campus Irchel,Off Y27J32, CH-8057 Zurich, Switzerland.
2019 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 68, no 1, p. 1-33Article in journal (Refereed) Published
Abstract [en]

For any fiat 2-category C, we show how its simple transitive 2-representations can be constructed using co-algebra 1-morphisms in the injective abelianization of C. Dually, we show that these can also be constructed using algebra 1-morphisms in the projective abelianization of C. We also extend Morita-Takeuchi theory to our setup and work out several examples, including that of Soergel bimodules for dihedral groups, explicitly.

Place, publisher, year, edition, pages
INDIANA UNIV MATH JOURNAL , 2019. Vol. 68, no 1, p. 1-33
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-379778DOI: 10.1512/iumj.2019.68.7554ISI: 000460124100001OAI: oai:DiVA.org:uu-379778DiVA, id: diva2:1297978
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationGöran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of TechnologyAvailable from: 2019-03-21 Created: 2019-03-21 Last updated: 2019-03-21Bibliographically approved

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Mazorchuk, Volodymyr

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