Cellular homology theorem
= Cellular homology theorem
{title2=$H_q(C_*^{\mathrm{cell}}(X))\cong H_q(X;\mathbb Z)$}
For a <CW complex>, the <homology> of its <cellular chain complex> naturally equals its <singular homology>. The relative groups of successive skeleton pairs, free on the cells in the corresponding dimension and zero in other dimensions, yield this identification through their connecting maps.