Abstract
We define torsion pairs for quasi-abelian categories and give several characterisations. We show that many of the torsion theoretic concepts translate from abelian categories to quasi-abelian categories. As an application, we generalise the recently defined algebraic Harder-Narasimhan filtrations to quasi-abelian categories.
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Acknowledgments
This work was undertaken as part of the author’s PhD studies supported by the EPSRC. The author thanks Sibylle Schroll and Hipolito Treffinger for many helpful discussions, Gustavo Jasso for communicating the proof of Proposition 4.8(b), and the anonymous referee for their comments.
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Presented by: Henning Krause
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Tattar, A. Torsion Pairs and Quasi-abelian Categories. Algebr Represent Theor 24, 1557–1581 (2021). https://doi.org/10.1007/s10468-020-10004-y
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DOI: https://doi.org/10.1007/s10468-020-10004-y