Morita base change in quantum groupoids

TL;DR

This paper introduces a method to transform quantum semigroupoids, specifically $ imes_R$-bialgebras, into equivalent forms using Morita equivalence, preserving their monoidal representation categories.

Contribution

It provides a procedure to perform Morita base change on quantum groupoids, maintaining their categorical properties and extending the understanding of their algebraic structures.

Findings

The Morita base change preserves the monoidal representation category.

The procedure applies to $ imes_R$-bialgebras and their Morita equivalent forms.

It generalizes the concept of base change in quantum algebra structures.

Abstract

Let $L$ be a quantum semigroupoid, more precisely a $\times_R$-bialgebra in the sense of Takeuchi. We describe a procedure replacing the algebra $R$ by any Morita equivalent, or in fact more generally any $\sqrt{\text{Morita}}$ equivalent (in the sense of Takeuchi) algebra $S$ to obtain a $\times_S$-bialgebra $\widetilde H$ with the same monoidal representation category.