Duality Theorem and Hom Functor in Braided Tensor Categories

TL;DR

This paper extends the Blatter-Montgomery duality theorem to braided tensor categories and demonstrates that the Hom functor preserves the braided Yetter-Drinfeld module structure.

Contribution

It generalizes the duality theorem to a broader categorical setting and establishes the Hom functor's compatibility with braided Yetter-Drinfeld modules.

Findings

Generalization of the duality theorem to braided tensor categories

Hom(V,W) inherits a braided Yetter-Drinfeld module structure

Provides new tools for studying modules in braided categories

Abstract

Blatter-Montgomery duality theorem is generalized into braided tensor categories. It is shown that $Hom(V,W)$ is a braided Yetter-Drinfeld module for any two braided Yetter-Drinfeld modules $V$ and $W$.