Functorial CW-approximation

Theorem 2.3.4 (CW-approximation, [Hirschhorn (2015), Theorem 2.1]). For every topological space \(X\), there exists a cell complex \(Z\) equipped with a weak homotopy equivalence \(q\colon Z \iso X\). Moreover, \(Z\) and \(q\) can be taken to be functorial in \(X\).