Kerodon

Remark 7.1.2.7. 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 7.1.1.11) 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 7.1.2.2. 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 $u$.