Idempotent Completions of n-Exangulated Categories

Suppose (C,E,s) ( C , E , s ) is an n -exangulated category. We show that the idempotent completion and the weak idempotent completion of C C are again n -exangulated categories. Furthermore, we also show that the canonical inclusion functor of C C into its (resp. weak) idempotent completion is n -exangulated and 2-universal among n -exangulated functors from (C,E,s) ( C , E , s ) to (resp. weakly) idempotent complete n -exangulated categories. Furthermore, we prove that if (C,E,s) ( C , E , s ) is n -exact, then so too is its (resp. weak) idempotent completion. We note that our methods of proof differ substantially from the extriangulated and $$(n+2)$$ ( n + 2 ) -angulated cases. However, our constructions recover the known structures in the established cases up to n -exangulated isomorphism of n -exangulated categories.