Finite type CW approximation
= Finite type CW approximation
{title2=$C\xrightarrow{\simeq_{\mathrm w}}X$}
For simply connected $X$ with finitely generated integral <homology> in every degree, the <Hurewicz theorem modulo a Serre class> gives finitely generated <homotopy groups>. Realize finite generating sets of successive relative <homotopy groups> by attaching finitely many cells at each stage. The resulting weak equivalence has finitely many cells in each dimension.