Exercise 9.1.5.6. Let $g: X \rightarrow S$ be Kan fibration between Kan complexes, where $S$ is connected and $X$ is contractible. Choose a vertex $s \in S$ and let $X_{s}$ denote the fiber $\{ s\} \times _{S} X$, so that we have a commutative diagram of Kan complexes

9.11

\begin{equation} \begin{gathered}\label{equation:impossible-lifting-problem} \xymatrix@R =50pt@C=50pt{ X_{s} \ar [r] \ar [d] & X \ar [d]^{f} \\ \{ s\} \ar [r] & S } \end{gathered} \end{equation}

Show that: