Abstract
We prove that certain subquotient categories of extriangulated categories are abelian. As a particular case, if an extriangulated category \(\mathscr {C}\) has a cluster-tilting subcategory \(\mathscr {X}\), then \(\mathscr {C}/\mathscr {X}\) is abelian. This unifies a result by Koenig and Zhu (Math. Z. 258 (2008) 143–160) for triangulated categories and a result by Demonet and Liu (J. Pure Appl. Algebra 217(12) (2013) 2282–2297) for exact categories.
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Acknowledgements
The authors would like to thank the referee for very helpful comments and advice in shaping the article into its present form. This work was supported by the Hunan Provincial Natural Science Foundation of China (Grant No. 2018JJ3205) and the NSF of China (Grant No. 11671221).
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Communicating Editor: Parameswaran Sankaran
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He, J., Zhou, P. Abelian quotients of extriangulated categories. Proc Math Sci 129, 61 (2019). https://doi.org/10.1007/s12044-019-0492-x
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DOI: https://doi.org/10.1007/s12044-019-0492-x