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Semi-abelian categories arising from pseudo cluster tilting subcategories (2309.04075v1)
Published 8 Sep 2023 in math.RT and math.CT
Abstract: The notion of a pseudo cluster tilting subcategory $\mathcal X$ in an extriangulated category $\mathcal C$ is defined in this article. We prove that the quotient category $\mathcal C/\mathcal X$, obtained by factoring an extriangulated category by a pseudo cluster tilting subcategory, is a semi-abelian category. Furthermore, we also show that the quotient category $\mathcal C/\mathcal X$ is an abelian category if and only if certain self-orthogonal conditions are satisfied. As an application, these results generalize the work of Xu and Zheng in the exact category.