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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the stable equivalences between finite tensor categories
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by Yuying Xu and Gongxiang Liu
Proc. Amer. Math. Soc. 151 (2023), 1867-1876
DOI: https://doi.org/10.1090/proc/16283
Published electronically: February 10, 2023

Abstract:

We aim to study Morita theory for tensor triangulated categories. For two finite tensor categories having no projective simple objects, we prove that their stable equivalence induced by an exact $\Bbbk \text {-}$linear monoidal functor can be lifted to a tensor equivalence under some certain conditions.
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Bibliographic Information
  • Yuying Xu
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • Email: yuyingxu@smail.nju.edu.cn
  • Gongxiang Liu
  • Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China
  • MR Author ID: 766485
  • Email: gxliu@nju.edu.cn
  • Received by editor(s): March 31, 2022
  • Received by editor(s) in revised form: July 23, 2022, and August 24, 2022
  • Published electronically: February 10, 2023
  • Additional Notes: The first author was supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province Grant KYCX22_0081. The second author was supported by National Natural Science Foundation of China (NSFC) Grant 12171230, 12271243.
    The first author is the corresponding author.
  • Communicated by: Sarah Witherspoon
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 1867-1876
  • MSC (2020): Primary 16T05, 18G65; Secondary 16G10, 18M05
  • DOI: https://doi.org/10.1090/proc/16283
  • MathSciNet review: 4556184