Example 4.6.6.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f_{\pm }: K_{-} \star K_{+} \rightarrow \operatorname{\mathcal{C}}$ be a diagram. Applying Theorem 4.6.6.5 in the special case $K = \Delta ^0$, we obtain an equivalence of $\infty $-categories
\[ \operatorname{\mathcal{C}}_{ f_{-} / \, / f_{+} } \rightarrow \operatorname{Fun}( K_{-} \star \Delta ^0 \star K_{+}, \operatorname{\mathcal{C}}) \times _{ \operatorname{Fun}( K_{-} \star K_{+}, \operatorname{\mathcal{C}}) } \{ f_{\pm } \} . \]