Duality for infinite-dimensional braided bialgebras and their (co)modules

TL;DR

This paper explores the duality theory for infinite-dimensional braided bialgebras and their (co)modules, detailing how dual objects inherit compatible braidings and how actions and coactions transform under duality.

Contribution

It provides a comprehensive framework for duality in infinite-dimensional braided structures, extending duality concepts to braided bialgebras and their modules and comodules.

Findings

Dual objects inherit compatible braidings from original structures.

Actions can be transformed into coactions on dual objects, and vice versa.

Framework applies to braided bialgebras and their module categories.

Abstract

The paper presents a detailed description of duality for braided algebras, coalgebras, bialgebras, Hopf algebras and their modules and comodules in the infinite setting. Assuming that the dual objects exist, it is shown how a given braiding induces compatible braidings for the dual objects, and how actions (resp. coactions) can be turned into coactions (resp. actions) of the dual coalgebra (resp. algebra), with an emphasis on braided bialgebras and their braided (co)module algebras.