Double cochain complex
= Double cochain complex
{title2=$d_h:D^{p,q}\to D^{p+1,q},\quad d_v:D^{p,q}\to D^{p,q+1}$}
Two degree-raising differentials square to zero and anticommute. If an initial convention uses commuting differentials, introduce a sign in one of them before forming the <total cochain complex>.