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".
|Name||Fields Institute communications|
|Publisher||American Mathematical Society|
|Workshop||Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories|
|Period||23/09/02 → 28/09/02|