Remark

Let G be a group, let F and $F'$ be abelian groups, let $\tau$ (resp. $\tau '$) be a group homomorphism from G to the automorphism group of F (resp. $F'$), and let $v: F\rightarrow F'$ be a group morphism such that

for $g\in G$ and $f\in F$. Let $\alpha$ be an element of Ex$_{\tau}(G,F)$. If the cocycle $c$ represents $\Theta (\alpha )$, then $v\circ c$ represents $\Theta (v_*(\alpha ))\in H^2(G,F')$.