Definition 9.2.7.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, and let $f: A \rightarrow B$ and $g: X \rightarrow Y$ be morphisms of $\operatorname{\mathcal{C}}$. We will say that $f$ is left orthogonal to $g$ if, for every lifting problem $\sigma :$
\[ \xymatrix@C =40pt@R=40pt{ A \ar [d]^{f} \ar [r] & X \ar [d]^{g} \\ B \ar [r] \ar@ {-->}[ur] & Y } \]
in the $\infty $-category $\operatorname{\mathcal{C}}$, the solution space $\operatorname{Sol}(\sigma )$ is a contractible Kan complex. In this case, we will also say that $g$ is right orthogonal to $f$.