ScalingStacks

Definition 3.2.1. For $d\geq-2$, a map of $\infty$-operads $f\colon\mathcal{O}\to\mathcal{U}$ is called a $d$-equivalence, if the induced map $h_{d+1}\left(f\right)\colon h_{d+1}\mathcal{O}\to h_{d+1}\mathcal{U}$ is an equivalence of $\infty$-operads, ie if it is essentially surjective on the underlying categories and induces an equivalence on the $d$-truncations of all the multi-mapping spaces.