Applied Categorical Structures

, Volume 22, Issue 5–6, pp 789–803 | Cite as

A Skew-Duoidal Eckmann-Hilton Argument and Quantum Categories

  • Stephen LackEmail author
  • Ross Street


A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories were originally defined as monoidal comonads on endomorphism objects in a particular monoidal bicategory . Then they were shown also to be skew monoidal structures (with an appropriate unit) on objects in . Now we see in what kind of quantum categories are merely monads.


Bialgebroid Fusion operator Quantum category Monoidal bicategory Duoidal category Monoidale Duoidale Skew-monoidal category Comonoid Hopf monad 

Mathematics Subject Classifications (2010)

18D10 18D05 16T15 17B37 20G42 81R50 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsMacquarie UniversityMacquarieAustralia

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