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I'm building a spectral sequence using an exact couple $D^1 \to D^1 \to E^1 \to D^1$, with $k$th derived exact couple $D^k \to D^k \to E^k \to D^k$. In this case, I happen to have more information about the $D^k$ piece than the $E^k$ piece, but I'm struggling to find references for facts I think are true relating information in $D^k$ to the whole spectral sequence, largely because $d_k$ already has a meaning in this context and Google can't tell the difference.

Is there a common name for the $D^k$ piece of a derived exact couple?

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    $\begingroup$ I’m aware only of the “rear” D and the “front” E. $\endgroup$
    – Eric Peterson
    Commented Sep 1, 2022 at 19:48

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