# Kerodon

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

Corollary 7.2.2.12. Let $e: A \rightarrow B$ be a morphism of simplicial sets and let $\operatorname{\mathcal{C}}$ be an $\infty$-category. If $e$ is left cofinal and $\operatorname{\mathcal{C}}$ admits $A$-indexed limits, then $\operatorname{\mathcal{C}}$ also admits $B$-indexed limits. If $e$ is right cofinal and $\operatorname{\mathcal{C}}$ admits $A$-indexed colimits, then $\operatorname{\mathcal{C}}$ also admits $B$-indexed colimits.