• Taking $L^\bullet = M^\bullet$ and using $R \to \mathop{\mathrm{Hom}}\nolimits ^\bullet (M^\bullet , M^\bullet )$ the map from the previous item becomes the evaluation map

$ev : K^\bullet \longrightarrow \mathop{\mathrm{Hom}}\nolimits ^\bullet (\mathop{\mathrm{Hom}}\nolimits ^\bullet (K^\bullet , M^\bullet ), M^\bullet )$

It sends $x \in K^ n$ to the map which sends $f \in \mathop{\mathrm{Hom}}\nolimits ^ m(K^\bullet , M^\bullet )$ to $(-1)^{nm}f(x)$.

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