Kerodon

Definition 7.1.1.11. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $u: K \rightarrow \operatorname{\mathcal{C}}$ be a diagram. We say that an object $Y \in \operatorname{\mathcal{C}}$ is a limit of $u$ if there exists a natural transformation $\alpha : \underline{Y} \rightarrow u$ which exhibits $Y$ as a limit of $u$, in the sense of Definition 7.1.1.1. We say that $Y$ is a colimit of $u$ if there exists a natural transformation $\beta : u \rightarrow \underline{Y}$ which exhibits $Y$ as a colimit of $u$.