Reversed dual chain complex
= Reversed dual chain complex
{title2=$X_i=\operatorname{Hom}_R(C_{-i},R),\quad d_X\phi=\phi d_C$}
The reversed <dual module> of a <chain complex> becomes a <chain complex> with the unsigned precomposition differential above. A functional on $C_{-i}$ is sent to a functional on $C_{1-i}$, lowering the reversed degree by one.