Shift of a cochain complex
= Shift of a cochain complex
{title2=$\Sigma E=E[1]$}
= Shifts of a cochain complex
{synonym}
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 $(-1)^r d_E$.