ScalingStacks

Theorem 1.1 (Eilenberg–Steenrod). Evaluation on a point, ${\sf ev}_{*}:\mathbf{H}(\spaces,{\sf Ch}^{\oplus})\rightarrow{\sf Ch}$, defines an equivalence between homology theories valued in chain complexes with direct sum and chain complexes. The inverse is given by singular homology, the functor assigning to a chain complex $V$ the functor $\mathsf{C}_{*}(-,V)$ of singular chains with coefficients in $V$.