Idempotent Completion of n-Angulated Categories

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