ScalingStacks

Definition 7.7.1.

For \(n\geq -1\), an \(n\)-operad is an \(\infty\)-operad all of whose multi-hom spaces, i.e. the \(\mathrm{Mul}_{\mathcal O}(X_1,\ldots, X_k; Y)\), are \((n-1)\)-truncated. We extend this to the case \(n=-2\) by declaring the terminal operad to be a \((-2)\)-operad. We denote the full subcategory of \(\mathrm{Op}\) on the \(n\)-operads by \(\mathrm{Op}_n\).