$n$-exact categories arising from $n$-exangulated categories

Let C be a Krull-Schmidt n-exangulated category and A be an n-extension closed subcategory of C . Then A inherits the n-exangulated structure from the given n-exangulated category in a natural way. 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. Furthermore, we also give a sufficient condition on when an n-exangulated category A is an n-exact category. These results generalize work by Klapproth and Zhou.

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