ScalingStacks

Proof. The composition of forgetful functors

$$\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{un}}}\to\mathbf{Op}_{\infty}\to\mathbf{Cat}_{\infty}$$

has a left adjoint given as the composition of the corresponding left adjoints. The first one takes $\Delta^{0}$ to $\mathbf{Triv}$ (by A.2.1.4.8) and the second takes $\mathbf{Triv}$ to $\mathbf{Triv}\otimes\mathbb{E}_{0}\simeq\mathbb{E}_{0}$ (by A.2.3.1.9). Hence, for every reduced operad $\mathcal{P}$ (which is in particular unital), we get

$$\operatorname{Map}\left(\mathbb{E}_{0},\mathcal{P}\right)\simeq\operatorname{Map}\left(\Delta^{0},\underline{\mathcal{P}}\right)\simeq\underline{\mathcal{P}}^{\simeq}\simeq\Delta^{0}.$$

∎