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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