Corollary 4.8.4.17. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $n$ be an integer, and let $A \subseteq B$ be simplicial sets. If $B$ has dimension $\leq n+1$, then every lifting problem
\[ \xymatrix@C =50pt@R=50pt{ A \ar [d] \ar [r] & \operatorname{\mathcal{C}}\ar [d] \\ B \ar [r] \ar@ {-->}[ur] & \mathrm{h}_{\mathit{\leq n}}\mathit{(\operatorname{\mathcal{C}})} } \]
has a solution. If $B$ has dimension $\leq n-1$, then the solution is unique.