Semi-abelian categories arising from pseudo cluster tilting subcategories

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.

15 pages