Duals of Ann-categories

TL;DR

This paper extends the concept of dual structures from monoidal categories to Ann-categories, showing that the dual of an Ann-category can be viewed as its center, which is braided.

Contribution

It generalizes the dual construction to Ann-categories and establishes that the dual of an Ann-category is its center, enriching the theory of categorical dualities.

Findings

The dual of an Ann-functor is constructed.

When the functor is the identity, the dual category is the center of the Ann-category.

The center of an Ann-category is a braided Ann-category.

Abstract

Dual monoidal category $\mathcal C^\ast$ of a monoidal functor $F:\mathcal C\to \mathcal V$ has been constructed by S. Majid. In this paper, we extend the construction of dual structures for an Ann-functor $F:\mathcal B\to \mathcal A$. In particular, when $F=id_{\mathcal A}$, then the dual category $\mathcal A^{\ast}$ is indeed the center of $\mathcal A$ and this is a braided Ann-category.