ScalingStacks

Remark 2.2.8. Observe that by 2.2.4, the projection $\mathbf{Op}_{\infty,*}^{\operatorname{\scriptsize{red}}}\to\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{red}}}$ is an equivalence. Hence, the inclusion $\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{red}}}\hookrightarrow\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{un}}}$ induces a functor

$$\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{red}}}\simeq\mathbf{Op}_{\infty,*}^{\operatorname{\scriptsize{red}}}\hookrightarrow\mathbf{Op}_{\infty,*}^{\operatorname{\scriptsize{un}}}.$$

Moreover, it exhibits $\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{red}}}$ as the full subcategory of $\mathbf{Op}_{\infty,*}^{\operatorname{\scriptsize{un}}}$ spanned by the reduced objects with respect to the underlying $\infty$-category functor $\underline{\left(-\right)}\colon\mathbf{Op}_{\infty,*}^{\operatorname{\scriptsize{un}}}\to\mathbf{Cat}_{\infty}$ in the sense of 2.1.4. Thus, the two notions of “reduced $\infty$-operad” coincide.