# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Example 7.2.4.5. 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 filtered. For a more general statement, see Proposition 7.2.7.1.