\begin{matrix}0 & \to & \widetilde{C}^0(G,A) & \xrightarrow{\partial^0} & \widetilde{C}^1(G,A) & \xrightarrow{\partial^1} & \widetilde{C}^2(G,A) & \to & \cdots\\ & & \downarrow ^{f^0} & & \downarrow ^{f^1} & & \downarrow ^{f^2} & &\\ 0 & \to & \widetilde{C}^0(G',A') & \xrightarrow{\partial^0} & \widetilde{C}^1(G',A') & \xrightarrow{\partial^1} & \widetilde{C}^2(G',A') & \to & \cdots\end{matrix}