Example 15.61.4. Let $K^\bullet , L^\bullet $ be objects of $D^{-}(R)$. Then there are spectral sequences

with $d_2^{p, q} : E_2^{p, q} \to E_2^{p + 2, q - 1}$ and

After replacing $K^\bullet $ and $L^\bullet $ by bounded above complexes of projectives, these spectral sequences are simply the two spectral sequences for computing the cohomology of $\text{Tot}(K^\bullet \otimes L^\bullet )$ discussed in Homology, Section 12.25.

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