ScalingStacks

Definition 3.4. Let $\mathcal{O}$ be an $\infty$-operad.

1. (1)

   For $d\geq 1$, we say that $\mathcal{O}$ is a $d$-operad if $\mathcal{O}^{\otimes}$ is a $d$-category.

2. (2)

   We say that $\mathcal{O}$ is a $0$-operad if $\mathcal{O}^{\otimes}$ is a skeletal $1$-category and $p$ is faithful.

3. (3)

   We say that $\mathcal{O}$ is a $(-1)$-operad if either $\mathcal{O}^{\otimes}=\varnothing$ or $p$ is an isomorphism.