Remark 9.1.5.3. In the situation of Lemma 9.1.5.2, condition $(\ast _{I})$ asserts that every diagram $I^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$ admits an extension to $(I^{\triangleleft } )^{\triangleright }$. This condition is automatically satisfied if $\operatorname{\mathcal{C}}$ is $\kappa $-filtered for some $\kappa $ larger than the cardinality of $I$. For a converse, see Proposition 9.1.5.8.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$