Kerodon

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

Notation 7.1.1.12. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $u: K \rightarrow \operatorname{\mathcal{C}}$ be a diagram. It follows from Proposition 7.1.1.11 that, if the diagram $f$ admits a limit $Y$, then the isomorphism class of the object $Y$ depends only on the diagram $u$. To emphasize this dependence, we will often denote $Y$ by $\varprojlim (u)$ and refer to it as the limit of the diagram $u$. Similarly, if $u$ admits a colimit $X \in \operatorname{\mathcal{C}}$, we will often denote $X$ by $\varinjlim (u)$ and refer to it as the colimit of the diagram $u$. Beware that this terminology is somewhat abusive, since the objects $\varprojlim (u)$ and $\varinjlim (u)$ are only well-defined up to isomorphism.