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February 28, 2026Algebra Colloquium0 citations

Semi-abelian Categories Arising from Pseudo Cluster Tilting Subcategories

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JHJian HeJHJing He

Key Points

  • The aim is to define pseudo cluster tilting subcategories and investigate their impact on quotient categories.
  • Define pseudo cluster tilting subcategories within extriangulated categories.
  • Formulate quotient categories by factoring extriangulated categories.
  • Establish conditions for the quotient category to be semi-abelian or abelian.
  • Proved that the quotient category obtained from an extriangulated category and a pseudo cluster tilting subcategory is semi-abelian.
  • Demonstrated that the quotient category is abelian under specific self-orthogonal conditions.
  • Generalized previous work on exact categories by Xu and Zheng.

Abstract

The notion of a pseudo cluster tilting subcategory in an extriangulated category is defined in this article. We prove that the quotient category Formula: see text, obtained by factoring an extriangulated category Formula: see text by a pseudo cluster tilting subcategory Formula: see text, is a semi-abelian category. Furthermore, we also show that the quotient category Formula: see text 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.

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Cite This Study

He et al. (2026) studied this question.

synapsesocial.com/papers/69a287e20a974eb0d3c03c55https://doi.org/10.1142/s1005386726000106
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