Remark 8.5.6.3. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a Morita equivalence of simplicial sets. Then $F$ is a weak homotopy equivalence: that is, for every Kan complex $X$, the induced map $\operatorname{Fun}( \operatorname{\mathcal{D}}, X) \rightarrow \operatorname{Fun}(\operatorname{\mathcal{C}}, X)$ is a homotopy equivalence. This is immediate from the definition, since $X$ is an idempotent complete $\infty $-category (Example 8.5.4.4).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$