Example Let $q: X \rightarrow S$ be a left fibration of simplicial sets and let $s \in S$ be a vertex. Then a morphism of Kan complexes $f: X_{s} \rightarrow X_{s}$ is given by covariant transport along the degenerate edge $\operatorname{id}_{s}: s \rightarrow s$ if and only if $f$ is homotopic to the the identity morphism $\operatorname{id}_{ X_ s}$.