Is $D$ symmetric monoidal?

TL;DR

This paper proves that a specific functor from symmetric spectra to chain complexes is symmetric monoidal, aiding the development of model category theory for these structures.

Contribution

It verifies the symmetric monoidal property of a key functor, facilitating advances in the model category theory of symmetric spectra and graded chain complexes.

Findings

The functor $D$ is symmetric monoidal.

Supports the development of model category theory.

Enhances understanding of symmetric spectra and chain complexes.

Abstract

We verify that a certain functor $D\colon\text{Sp}^\Sigma(\text{Ch}^+)\to\text{Ch}$ 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 $\mathbb{Z}$.