A note on coring extensions

TL;DR

This paper introduces the concept of coring extensions, relating them to functors between comodule categories and descent data, and establishes a categorical framework for these structures.

Contribution

It defines coring extensions and links them to factorisable functors, providing a categorical perspective on corings and their morphisms.

Findings

Corings are related to additive functors between comodule categories.

A categorical framework for corings and coring extensions is developed.

Connections to descent data are illustrated.

Abstract

A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable functors is illustrated by functors between categories of descent data. A category in which objects are corings and morphisms are coring extensions is also introduced.