Quantum categories, star autonomy, and quantum groupoids
Abstract
Description
A useful general concept of bialgebroid seems to be resolving itself in recent publications; we give a treatment in terms of modules and enriched categories. We define the term "quantum category". The definition of antipode for a bialgebroid is less resolved in the literature. Our suggestion is that the kind of dualization occurring in Barr's star-autonomous categories is more suitable than autonomy (= compactness = rigidity). This leads to our definition of quantum groupoid intended as a "Hopf algebra with several objects".
41 pages, PDF file based on MacWrite document This revised version corrects some duality mistakes in the last three sections
41 pages, PDF file based on MacWrite document This revised version corrects some duality mistakes in the last three sections