ScalingStacks

Definition 3.2.2. For $d\geq-2$, an $\infty$-operad $\mathcal{O}$ is called $d$-connected if the unique map from $\mathcal{O}$ to the terminal $\infty$-operad $\mathbb{E}_{\infty}$ is a $d$-equivalence, ie if all the multi-mapping spaces in $\mathcal{O}$ are $d$-connected.