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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 16th 2013

    at braided monoidal 2-categiry the following query box was sitting, which I hereby move from there to here

    +–{: .query} Ben Webster: I would very much like to know: what structure on a (triangulated/dg-/stable infinity/whatever you like) monoidal category would make its 2-category of module categories (give that phrase any sensible construal you like) is braided monoidal.

    If one decategorifies this question, one gets the question “what structure on a ring makes its category of representations braided monoidal” and the answer to this question is well-known: a quasi-triangular quasi-Hopf structure.

    I asked a MathOverflow question on the same topic. No interesting answers yet. =–

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 19th 2014
    • (edited Jun 19th 2014)

    Today I had had again the pleasure to chat with Larry Breen. In passing he reminded me that he had proposed the definition of braided monoidal (2-)category independently of Joyaj-Street in a letter to Deligne in 1988, as linked to from his webpage.

    I have added this pointer to the nLab entries here and here.

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