Quotients of extriangulated categories by hereditary-type subcategories are quasi-abelian, and abelian precisely when the subcategory is cluster tilting in a relative extriangulated structure.
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Quasi-abelian quotients in extriangulated categories
Quotients of extriangulated categories by hereditary-type subcategories are quasi-abelian, and abelian precisely when the subcategory is cluster tilting in a relative extriangulated structure.