Extensions subcategories of wide subcategories in abelian category

Let [Formula: see text] be an abelian category. The main theme of this paper is to study extensions of wide subcategories in [Formula: see text]. We characterize the extension subcategory [Formula: see text] defined by wide subcategories [Formula: see text] and [Formula: see text], which generalizes Yoshizawa’s work. Moreover, we provide a criterion for wide filtered subcategories to decompose into an extension of two wide filtered subcategories.