Universal coefficient theorem for cohomology
= Universal coefficient theorem for cohomology
This is the cohomological form of the <universal coefficient theorem>, with Ext and Hom terms rather than the homological tensor and Tor terms.
For an abelian coefficient group $G$, cohomology fits into a split short exact sequence
$$
0\to\operatorname{Ext}(H_{n-1}(X;\mathbb Z),G)
\to H^n(X;G)
\to\operatorname{Hom}(H_n(X;\mathbb Z),G)\to0.
$$