Semi-abelian categories arising from pseudo cluster tilting subcategories

TL;DR

This paper introduces pseudo cluster tilting subcategories in extriangulated categories and proves that their quotients are semi-abelian, becoming abelian under specific conditions, thus generalizing existing results in exact categories.

Contribution

It defines pseudo cluster tilting subcategories in extriangulated categories and shows their quotients are semi-abelian, extending prior work to a broader categorical context.

Findings

Quotients by pseudo cluster tilting subcategories are semi-abelian.

The quotient is abelian if certain self-orthogonal conditions hold.

Generalization of Xu and Zheng's results to extriangulated categories.

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.