n-exact Categories Arising from n-exangulated Categories

Let \({\cal C}\) be a Krull–Schmidt n-exangulated category and \({\cal A}\) be an n-extension closed subcategory of \({\cal C}\). Then \({\cal A}\) inherits the n-exangulated structure from the given n-exangulated category in a natural way. This construction gives n-exangulated categories which are neither n-exact categories in the sense of Jasso nor (n + 2)-angulated categories in the sense of Geiss–Keller–Oppermann in general. Furthermore, we also give a sufficient condition on when an n-exangulated category \({\cal A}\) is an n-exact category. These results generalize work by Klapproth and Zhou.