A skew-duoidal Eckmann-Hilton argument and quantum categories

Stephen Lack*, Ross Street

*Corresponding author for this work

    Research output: Contribution to journalArticle

    2 Citations (Scopus)


    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 ℳ. Then they were shown also to be skew monoidal structures (with an appropriate unit) on objects in ℳ. Now we see in what kind of ℳ quantum categories are merely monads.

    Original languageEnglish
    Pages (from-to)789-803
    Number of pages15
    JournalApplied Categorical Structures
    Issue number5-6
    Publication statusPublished - Oct 2014

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