Proposition 9.6.7.4. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing $2$-simplices $\sigma $ and $\sigma '$, which we depict as
\[ \xymatrix@R =50pt@C=50pt{ & Y \ar [dr]^{g} & & & Y' \ar [dr]^{g'} & \\ X \ar [ur]^{f} \ar [rr]^{h} & & Z & X' \ar [ur]^{f'} \ar [rr]^{h'} & & Z'. } \]
If $f$ is left orthogonal to $g'$, then the restriction map
\[ \theta : \operatorname{Hom}_{ \operatorname{Fun}( \Delta ^2, \operatorname{\mathcal{C}}) }( \sigma , \sigma ' ) \rightarrow \operatorname{Hom}_{ \operatorname{Fun}( \Delta ^1, \operatorname{\mathcal{C}}) }( h, h' ) \]
is a homotopy equivalence.