Example 9.1.1.6. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which contains a final object $X$. Then every morphism of simplicial sets $f: K \rightarrow \operatorname{\mathcal{C}}$ can be extended to a morphism $\overline{f}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ which carries the cone point of $K^{\triangleright }$ to the object $X$. In particular, the $\infty $-category $\operatorname{\mathcal{C}}$ is $\kappa $-filtered for every infinite cardinal $\kappa $. For a more general statement, see Proposition 9.1.6.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$