Corollary 8.5.6.5. For every $\infty $-category $\operatorname{\mathcal{C}}$, evaluation on the non-identity morphism of $\operatorname{Idem}$ induces a bijection
\[ \theta : \pi _0( \operatorname{Fun}( \operatorname{N}_{\bullet }( \operatorname{Idem}), \operatorname{\mathcal{C}})^{\simeq } ) \rightarrow \pi _0( (\operatorname{End}_{\operatorname{\mathcal{C}}}^{\mathrm{idm} })^{\simeq } ). \]