A map i\colon A \to X of topological spaces is called a cofibrationpg 51 if for any map f:A \to S such that there is an extension to X, meaning there is a map f':X \to S such that f'\circ i = f, we can extend a homotopy of maps H:A\times I \to S to a homotopy of maps H': X\times I \to S, where\begin{align}
