Corings with exact rational functors and injective objects

TL;DR

This paper explores the relationship between localization in module categories and injective comodules over specific corings, with applications to Doi-Koppinen modules, extending existing results.

Contribution

It introduces new insights into the structure of injective comodules over certain corings and generalizes prior findings in the context of Doi-Koppinen modules.

Findings

Established connections between localization and injective comodules

Generalized results for Doi-Koppinen modules

Provided new theoretical tools for coring analysis

Abstract

We describe how some aspects of abstract localization on module categories have applications to the study of injective comodules over some special types of corings. We specialize the general results to the case of Doi-Koppinen modules, generalizing previous results in this setting.