Notation Let $q: X \rightarrow S$ be a right fibration of simplicial sets, and let $e: s \rightarrow s'$ be an edge of the simplicial set $S$. We will often use the symbol $e^{\ast }$ to denote a morphism of Kan complexes $X_{s'} \rightarrow X_{s}$ which is given by covariant transport along $e$. By virtue of Proposition, such a morphism exists and is uniquely determined up to homotopy.