# Graded change of ring

## TL;DR

This paper explores the properties of scalar restriction, extension, and coextension functors in graded modules, examining their interactions with various graded constructions to characterize epimorphisms of graded rings.

## Contribution

It provides new characterizations of epimorphisms of graded rings through the analysis of scalar functors and their interactions with graded tensor and Hom functors.

## Key findings

- Characterizations of epimorphisms of graded rings
- Analysis of scalar functors in graded module categories
- Interactions between graded functors and ring morphisms

## Abstract

We investigate scalar restriction, scalar extension, and scalar coextension functors for graded modules, including their interplay with coarsening functors, graded tensor products, and graded Hom functors. This leads to several characterisations of epimorphisms of graded rings.