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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 31st 2014

    the entry modular tensor category was lacking (among many things that it is still lacking) some pointers to literature that reviews the relation to QFT. I have added a handful, maybe the best one is this here:

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 16th 2014
    • (edited Jul 16th 2014)

    I see that the entry modular tensor category is full of trivial typos in the text. I am too quasi-offline now to do anything about it, though. Maybe tomorrow. That entry could generally use a bit of attention.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 17th 2014

    Fixed some typos.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 17th 2014


    • CommentRowNumber5.
    • CommentAuthorJoe Moeller
    • CommentTimeFeb 2nd 2020
    The string diagram in the definition appears to be broken.
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2021

    added pointer to:

    • Colleen Delaney, Lecture notes on modular tensor categories and braid group representations, 2019 (pdf)

    diff, v15, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2021

    added pointer to:

    diff, v15, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2021

    added pointer to the original article:

    diff, v15, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMay 14th 2022
    • (edited May 14th 2022)


    It is readily plausible that

    the structure of a braided tensor category (and thus also that of a modular tensor category) on [ the rep categ. of a VOA ] is entirely fixed by the genus zero conformal blocks.

    (here quoted from p. 36 of Ingo Runkel’s “Algebra in Braided Tensor Categories and Conformal Field Theory”, where the evident idea is indicated).

    What would be a good citation of this fact as a theorem with a proof?

    (I know to sift through the canonical sources on the matter, but maybe somebody knows direct pointer to volume, page and verse where this is citably proven.)

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 15th 2022

    added a brief mentioning of this statement to the entry (here)

    diff, v16, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeMay 16th 2022

    added pointers to


    and used these to slightly expand the paragraph on VOAs (here)

    diff, v18, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJun 10th 2022

    added further original references on the construction of MTCs as VOA-representation categories:

    diff, v21, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2022

    added pointer to:

    diff, v23, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 7th 2023

    added pointer to:

    diff, v25, current