ScalingStacks

Lemma 2.2.3. The restriction of the forgetful functor $\underline{\left(-\right)}\colon\mathbf{Op}_{\infty}^{\operatorname{\scriptsize{un}}}\to\mathbf{Cat}_{\infty}$ admits a right adjoint that takes every $\infty$-category $\mathcal{C}$ to the coCartesian $\infty$-operad $\mathcal{C}_{\sqcup}$ and the unit map of the adjunction $\underline{\mathcal{C}_{\sqcup}}\to\mathcal{C}$ is an equivalence (ie $\left(-\right)_{\sqcup}$ is fully faithful).