ScalingStacks

Corollary 4.2.7. In a presentable $\infty$-category $\mathcal{C}$, an object $X$ is $n$-connected for some $n\geq-2$ if and only if its $n$-truncation $\tau_{\leq n}^{\mathcal{C}}X$ is a terminal object of $\mathcal{C}$.