Adjoint and Frobenius Pairs of Functors for Corings

TL;DR

This paper explores the relationships between categories of comodules over corings, focusing on adjoint and Frobenius pairs, and introduces a new concept of Frobenius coring extension with applications to entwining structures and graded rings.

Contribution

It introduces a general framework for adjoint and Frobenius pairs of functors between coring comodules and defines Frobenius coring extensions, extending previous theories.

Findings

New characterization of Frobenius coring extensions

Application to entwining structures yields novel results

Connections established with graded ring theory

Abstract

We investigate adjoint and Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads to a reasonable notion of Frobenius coring extension. When applied to corings stemming from entwining structures, we obtain new results in this setting and in graded ring theory.