Monoidal categories of comodules for coquasi Hopf algebras and Radford's formula

TL;DR

This paper explores the monoidal structure of comodules over coquasi Hopf algebras, proving Radford's S^4 formula via categorical methods and establishing equivalences between comodules and Hopf modules.

Contribution

It provides a categorical proof of Radford's S^4 formula for finite dimensional coquasi Hopf algebras and analyzes the monoidal properties of the category of Hopf modules.

Findings

Monoidal equivalence between comodules and Hopf modules.

Categorical proof of Radford's S^4 formula.

Double dual functor isomorphism.

Abstract

We study the basic monoidal properties of the category of Hopf modules for a coquasi Hopf algebra. In particular we discuss the so called fundamental theorem that establishes a monoidal equivalence between the category of comodules and the category of Hopf modules. We present a categorical proof of Radford's $S^4$ formula for the case of a finite dimensional coquasi Hopf algebra, by establishing a monoidal isomorphism between certain double dual functors.