Exercise 2.7.3 of Prof. Weibel H-Book is wrong. Suggestion for an errata. In this exercise, we have to prove that there is an isomorphism $$\text{Hom}(\text{Tot}^{\oplus}(P\otimes Q),I)\cong \text{Hom}(P,\text{Tot}^{\prod}(\text{Hom}(Q,I))$$ of double complexes. But if I choose $I$ to be the cochain complex with only $I_0$ (all the other abelian groups of other degree equals to zero) I get $$\text{Hom}(\text{Tot}^{\oplus}(P\otimes Q),I)_{p,q}=\prod_n\text{Hom}(P_{p-n},\text{Hom}(Q_n,I_q))$$ which is $0$ if $q\neq 0$ and $$\text{Hom}(P,\text{Tot}^{\prod}(\text{Hom}(Q,I))_{p,q}=\text{Hom}(P_p,\text{Hom}(Q_{q},I_0))=\text{Hom}(P_p\otimes Q_q,I_0)$$ and they clearly differs. Where am I wrong ?

Actually, the only way I can make this exercise works is by symmetrizing further the two expressions by looking at the $\text{Tot}^{\prod}$ of each terms of the equality.

So we get $$\text{Tot}^{\prod}(\text{Hom}(\text{Tot}^{\oplus}(P\otimes Q),I))\cong \text{Tot}^{\prod}(\text{Hom}(P,\text{Tot}^{\prod}(\text{Hom}(Q,I)))$$

which should be added in the Errata for the H-Book of Prof. Weibel to save us a lot of time !