ScalingStacks

Definition 3.1. Let $d\geq-1$. An essentially $d$-operad is an $\infty$-operad $\mathcal{O}$ such that for all $X_{1},\dots,X_{n},Y\in\underline{\mathcal{O}}$, the multi-mapping space $\mbox{Mul}_{\mathcal{O}}\left(\left\{X_{1},\dots,X_{n}\right\};Y\right)$ is $\left(d-1\right)$-truncated. We denote by $\mathbf{Op}_{d}$ the full subcategory of $\mathbf{Op}_{\infty}$ spanned by essentially $d$ -operads.