This is probably a very basic question, but I can't wrap my head around it.
Given a normal open subgroup $U$ of a profinite group $G$ and a $G$-Module $A$ we have the following equation in group cohomology: $\operatorname{res}^G_U \circ \operatorname{cor}^U_G = N_{G/U}$
This follows immediately from the double coset formula (see NSW: Cohomology of Number Fields p.49).
My problem is twofold:
What does $N_{G/U}$ mean in this context? Is it induced by dimension shifting from the case $n=0$: $N_{G/U}: A^U \rightarrow A^G$?
And if this interpretation is correct:Is the induced homomorphism $N_{G/U}$ in some way equivalent or equal to $\operatorname{cor}^U_G$ which in the case $n=0$ is the above norm?