Let \({\mathcal {C}}\) be an n-angulated category. We prove that its idempotent completion \(\widetilde{{\mathcal {C}}}\) admits a unique n-angulated structure such that the canonical functor \(\iota : {\mathcal {C}}\rightarrow \widetilde{{\mathcal {C}}}\) is n-angulated. Moreover, the functor \(\iota \) induces an equivalence \(Hom _{n-ang }(\widetilde{{\mathcal {C}}},{\mathcal {D}})\cong Hom _{n-ang }({\mathcal {C}},{\mathcal {D}})\) for any idempotent complete n-angulated category \({\mathcal {D}}\), where \(Hom _{n-ang }\) denotes the category of n-angulated functors.

令\（{\ mathcal {C}} \）为n角类别。我们证明了它的幂等补全\（\ widetilde {{\ mathcal {C}}} \\）接受一个唯一的n角结构，使得规范函子\ {\ iota：{\ mathcal {C}} \ rightarrow \ widetilde { {\ mathcal {C}}} \）的角度为n。此外，函子\（\ iota \）引起等价\（Hom _ {n-ang}（\ widetilde {{\ mathcal {C}}}，{\ mathcal {D}}）\ cong Hom _ {n- ang}（{{mathcal {C}}，{\ mathcal {D}}）\）表示任何幂等的完整n角度分类\（{\ mathcal {D}} \），其中\（Hom _ {n-ang } \）表示以下类别n角函子。