ScalingStacks

Definition 4.2.4. For $n\geq-2$, a map $f\colon A\to B$ in an $\infty$-category $\mathcal{C}$ is $n$-connected if it is left orthogonal to every $n$-truncated map; ie for every commutative square $q\colon\Delta^{1}\times\Delta^{1}\to\mathcal{C}$,

in which $g$ is $n$-truncated, $L\left(q\right)$ is contractible. An object $A\in\mathcal{C}$ is called $n$-connected if $A\to\text{pt}_{\mathcal{C}}$ is $n$-connected.