Quantum categories, star autonomy, and quantum groupoids
By Brian Day, Ross Street. 2003
75 citations recorded by the source corpus.
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".
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4524b29f3e635db69c6c1c7c4983cd5d982b9c90
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In Algebra and Number Theory
In Geometry and Topology
- Ross Street
- Stephen Lack
- Michael Batanin
- Mark Weber
- Aaron D. Lauda
- Bob Coecke
- C. Berger
- Joachim Kock
In Mathematical Physics
- Ross Street
- Stephen Lack
- Michael Batanin
- Mark Weber
- Aaron D. Lauda
- Bob Coecke
- C. Berger
- Joachim Kock
Citations in the corpus
- Skew monoidales, skew warpings and quantum categories (2012, unknown): “s) in any monoidal bicategory M. These are skew-monoidal categories when M is Cat. Our main results are presented at the level of monoidal bicategories. However, aconsequenceis that quantum categories[10] with basecomonoid C in a suitably complete braided monoidal category V are precisely skew monoi”
- Frobenius algebras and ambidextrous adjunctions (2005, unknown): “These ∗-autonomous monoidal categories are known to have an interesting relationship with quantum groups and quantum groupoids [ 8 ].”
- Skew-closed categories (2012, background): “[13]) could be characterized in terms of skew-monoidal structures on the category of one-sided R-modules for which the lax unit was Ritself. More generally, it is shown in [9] that quantum categories [4] with base comonoid Cin a suitably complete braided monoidal category V are precisely skewmonoida”