Shift of a cochain complex ($\Sigma E=E[1]$)

The shift $E[1]$ has $E[1{]}^i=E^{i+1}$ and differential $-d_E^{i+1}$. Thus $H^i(E[1])=H^{i+1}(E)$. In general the differential of $E[r]$ is $(-1{)}^r{d}_E$.