Hopf rings for grading and differentials

TL;DR

This paper generalizes the construction of a Hopf ring for differential graded abelian groups to broader symmetric monoidal additive categories, combining grading and differential structures via semidirect products.

Contribution

It introduces a method to obtain Hopf rings for graded and differential structures through semidirect products in general symmetric monoidal additive categories.

Findings

Hopf ring construction extends beyond abelian groups

Semidirect product combines grading and differential structures

Applicable in broad symmetric monoidal additive categories

Abstract

In the category of abelian groups, Pareigis constructed a Hopf ring whose comodules are differential graded abelian groups. We show that this Hopf ring can be obtained by combining grading and differential Hopf rings using semidirect product in fairly general symmetric monoidal additive categories.