Total cochain complex
= Total cochain complex
{title2=$\operatorname{Tot}^nD=\bigoplus_{p+q=n}D^{p,q}$}
The total differential is $d_h+d_v$ for anticommuting differentials. For a <double cochain complex> bounded in both indices, both index filtrations are finite and have the same total <cohomology> as abutment.