ScalingStacks

Definition 2.2.1. (A.2.3.1.1, A.2.3.4.1) An $\infty$-operad $\mathcal{O}$ is called:

1. (1)

   Unital if for every object $X$ of $\underline{\mathcal{O}}$, the space of constants $\text{Mul}_{\mathcal{O}}\left(\varnothing,X\right)$ is contractible. We denote the full $\infty$-category spanned by the unital $\infty$-operads by $\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{un}}}$.

2. (2)

   Reduced if it is unital and the underlying $\infty$-category is a contractible space. We denote the full $\infty$-category spanned by the reduced $\infty$-operads by $\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{red}}}$.