N-extension closed subcategories of $$(n+2)$$-angulated categories

Abstract

Let \({\mathscr {C}}\) be a Krull-Schmidt \((n+2)\)-angulated category and \({\mathscr {A}}\) be an n-extension closed subcategory of \({\mathscr {C}}\). Then \({\mathscr {A}}\) has the structure of an n-exangulated category in the sense of Herschend–Liu–Nakaoka. This construction gives n-exangulated categories which are not n-exact categories in the sense of Jasso nor \((n+2)\)-angulated categories in the sense of Geiss–Keller–Oppermann in general. As an application, our result can lead to a recent main result of Klapproth