Morita base change in quantum groupoids

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 $\tilde{H}$ with the same monoidal representation category.

19 pages