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We show that the idempotent completion and the weak idempotent completion of $$\\mathcal {C}$$<\/jats:tex-math>\n C<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> are again n<\/jats:italic>-exangulated categories. Furthermore, we also show that the canonical inclusion functor of $$\\mathcal {C}$$<\/jats:tex-math>\n C<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> into its (resp. weak) idempotent completion is n<\/jats:italic>-exangulated and 2-universal among n<\/jats:italic>-exangulated functors from $$(\\mathcal {C},\\mathbb {E},\\mathfrak {s})$$<\/jats:tex-math>\n \n (<\/mml:mo>\n C<\/mml:mi>\n ,<\/mml:mo>\n E<\/mml:mi>\n ,<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to (resp. weakly) idempotent complete n<\/jats:italic>-exangulated categories. Furthermore, we prove that if $$(\\mathcal {C},\\mathbb {E},\\mathfrak {s})$$<\/jats:tex-math>\n \n (<\/mml:mo>\n C<\/mml:mi>\n ,<\/mml:mo>\n E<\/mml:mi>\n ,<\/mml:mo>\n s<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is n<\/jats:italic>-exact, then so too is its (resp. weak) idempotent completion. We note that our methods of proof differ substantially from the extriangulated and $$(n+2)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n n<\/mml:mi>\n +<\/mml:mo>\n 2<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-angulated cases. However, our constructions recover the known structures in the established cases up to n<\/jats:italic>-exangulated isomorphism of n<\/jats:italic>-exangulated categories.<\/jats:p>","DOI":"10.1007\/s10485-023-09758-5","type":"journal-article","created":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T18:02:16Z","timestamp":1707415336000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Idempotent Completions of n-Exangulated Categories"],"prefix":"10.1007","volume":"32","author":[{"given":"Carlo","family":"Klapproth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dixy","family":"Msapato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amit","family":"Shah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,2,8]]},"reference":[{"key":"9758_CR1","doi-asserted-by":"crossref","unstructured":"Anderson, F. 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