Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 7.1.4.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $u: K \rightarrow \operatorname{\mathcal{C}}$ be a diagram. Then an object $Y \in \operatorname{\mathcal{C}}$ is a limit of $u$ (in the sense of Definition 7.1.1.10) if and only if there exists a diagram $\overline{u}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{C}}$ which exhibits $Y$ as a limit of $u$. This is a reformulation of Corollary 7.1.4.2. Similarly, $Y$ is a colimit of $u$ if and only if there exists a diagram $\overline{u}': K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ which exhibits $Y$ as a colimit of $u$.