Definition 3.6.6.1. Let $q: X \rightarrow S$ be a continuous function between topological spaces. We say that $q$ is a Serre fibration if, for every integer $n \geq 0$, every lifting problem
\[ \xymatrix@R =50pt@C=50pt{ \{ 0\} \times | \Delta ^ n | \ar [r] \ar [d] & X \ar [d]^{q} \\ \empty [0,1] \times | \Delta ^ n | \ar [r] \ar@ {-->}[ur] & S } \]
admits a solution.