Filtered cochain complex
= Filtered cochain complex
{title2=$\cdots\supseteq F^pC\supseteq F^{p+1}C\supseteq\cdots$}
= Filtration on a cochain complex
{synonym}
A <cochain complex> with a decreasing filtration by <cochain subcomplexes>. A filtration finite in each degree is bounded in the degreewise sense; uniform bounds $F^aC=C$ and $F^bC=0$ are sufficient. The associated <spectral sequence> starts with the graded quotient complexes.