Let $f:G'\to G$ be a group homomorphism and let $A$ be a $G$-module.
We regard $A$ as a $G'$-module via restriction of scalars along $f$.
I am struggling to understand the following statement:
"$f$ induces group homomorphisms $H^q(G,A)\to H^q(G',A)$ for each $q\geq 0.$"
For each $q\geq 0$ there is a natural group homomorphism
These induce (as they compatible with the standard resolutions) group homomorphisms
Doesn't this mean the induced map for $q=0$ is just the identity (edit: inclusion, not identity) map?