Weak Hopf monoids in braided monoidal categories

TL;DR

This paper develops the theory of weak bimonoids and weak Hopf monoids in braided monoidal categories, establishing their connections to quantum categories and quantum groupoids, and constructing examples from Frobenius monoids.

Contribution

It introduces the theory of weak bimonoids and weak Hopf monoids in braided monoidal categories, linking them to quantum categories and quantum groupoids, and provides a construction from Frobenius monoids.

Findings

Weak Hopf monoids are quantum groupoids.

Separable Frobenius monoids lead to weak Hopf monoids.

The theory connects algebraic structures with quantum categorical concepts.

Abstract

We develop the theory of weak bimonoids in braided monoidal categories and show them to be quantum categories in a certain sense. Weak Hopf monoids are shown to be quantum groupoids. Each separable Frobenius monoid R leads to a weak Hopf monoid R \otimes R.