Is $D$ symmetric monoidal?

Abstract

We verify that a certain functor $D:{\text{Sp}}^{\Sigma }({\text{Ch}}^{+})\to \text{Ch}$ is symmetric monoidal. This functor is used elsewhere in developing the model category theory of symmetric spectra and of chain complexes graded over $\mathbb{N}$ or $\mathbb{Z}$.

This is a very old note, which has been circulating privately. I have been asked to upload it so that people can refer to it