I think this is a pretty simple question, but I cannot seem to find the answer anywhere:
In the context of group cohomology of a group $G$, $G$-invariant maps are often mentioned. What is the definition of $G$-invariant. Also, is it true that maps need to be $G$-invariant between cochains to make the maps carry through to the cohomology groups (I remember reading this somewhere, but I cannot find this either)
Thank you for any help.