Quantum categories, star autonomy, and quantum groupoids

Details Quantum categories, star autonomy, and quantum groupoids Quantum categories, star autonomy, and quantum groupoids

2003-01-20

arxiv.org/abs/math/0301209v2

Mathematics

Category Theory

41 pages, PDF file based on MacWrite document This revised version corrects some duality mistakes in the last three sections

Scientific paper

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".

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