Corollary 8.5.9.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then composition with the partial idempotent $\iota $ of Notation 8.5.9.4 induces a trivial Kan fibration of $\infty $-categories
\[ \operatorname{Fun}( \operatorname{N}_{\bullet }^{\operatorname{D}}( B \mathrm{Dy} ), \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}( \operatorname{N}_{\leq 2}(\operatorname{Idem}), \operatorname{\mathcal{C}}). \]