Exact sequences of tensor categories with respect to a module category
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Etingof_Exact sequences.pdf
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Author(s)
Etingof, Pavel I
Gelaki, Shlomo
Date Issued
January 2017
Journal
Advances in Mathematics
Publisher
Elsevier BV
Citation
Etingof, Pavel and Shlomo Gelaki. “Exact Sequences of Tensor Categories with Respect to a Module Category.” Advances in Mathematics 308 (February 2017): 1187–1208 © 2016 Elsevier Inc
Version
Original manuscript
Abstract
We generalize the definition of an exact sequence of tensor categories due to Bruguières and Natale, and introduce a new notion of an exact sequence of (finite) tensor categories with respect to a module category. We give three definitions of this notion and show their equivalence. In particular, the Deligne tensor product of tensor categories gives rise to an exact sequence in our sense. We also show that the dual to an exact sequence in our sense is again an exact sequence. This generalizes the corresponding statement for exact sequences of Hopf algebras. Finally, we show that the middle term of an exact sequence is semisimple if so are the other two terms. Keywords: Tensor categories; Module categories
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.AIM.2016.12.021
