Example 9.2.7.5. Let $\operatorname{\mathcal{C}}$ be an ordinary category. Then a morphism $f: A \rightarrow B$ is left orthogonal to a morphism $g: X \rightarrow Y$ in the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ if and only if every lifting problem
\[ \xymatrix@C =40pt@R=40pt{ A \ar [d]^{f} \ar [r]^-{u_0} & X \ar [d]^{g} \\ B \ar [r]^-{\overline{u}} \ar@ {-->}[ur] & Y } \]
admits a unique solution: that is, there is a unique morphism $u: B \rightarrow X$ satisfying $u \circ f = u_0$ and $g \circ u = \overline{u}$.