Quotients of extriangulated categories induced by selforthogonal subcategories

TL;DR

This paper explores how certain quotient categories derived from extriangulated categories, based on selforthogonal subcategories, can be equivalent to module categories and may be abelian under specific conditions, generalizing previous results.

Contribution

It establishes equivalences between quotient categories of extriangulated categories and module categories, extending known results to broader contexts with selforthogonal subcategories.

Findings

Quotient categories are equivalent to module categories via functors E and Hom.

If the subcategory is contravariantly finite, the quotient category becomes abelian.

Generalizes results by Demonet-Liu and Zhou-Zhu.

Abstract

Let C be an extriangulated category. We prove that two quotient categories of extriangu?lated categories induced by selforthogonal subcategories are equivalent to module categories by restriction of two functors E and Hom, respectively. Moreover, if the selforthogonal sub?category is contravariantly finite, then one of the two quotient categories is abelian. This result can be regarded as a generalization of Demonet-Liu and Zhou-Zhu.