Lemma 7.1.8. ([Lur17, Prop. 2.4.3.9, Cor. 2.4.3.11], [SY19, Lem. 2.2.3]).
The assignment \(\mathcal C\mapsto \mathcal C_{\sqcup}\) induces a fully faithful functor \(\mathrm{Cat}_{\infty}\hookrightarrow \mathrm{Op}^{\mathrm{un}}\) which is right adjoint to the underlying-category functor \(\mathrm{Op}^{\mathrm{un}}\rightarrow\mathrm{Cat}_{\infty}\).