Universal coefficient theorem for homology
= Universal coefficient theorem for homology
For an abelian coefficient group $G$, there is a split short exact sequence
$$
0\to H_i(X;\mathbb Z)\otimes G
\to H_i(X;G)
\to\operatorname{Tor}(H_{i-1}(X;\mathbb Z),G)\to0.
$$
For $G=\mathbb Q$, the Tor term vanishes.
This is the homology case of the <universal coefficient theorem>; its cohomology case uses Hom and Ext rather than tensor product and Tor.