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All 3D TQFTs I know of are of Reshetikhin-Turaev type. These are fully extended and I wondered if there are known examples of TQFTs such that there is no once-extended TQFT extending it.

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    $\begingroup$ This question and its answers discuss a nonextendable theory in the 2D case. $\endgroup$
    – Arun Debray
    Jan 16, 2018 at 17:29
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    $\begingroup$ Also, is it true that Reshetikhin-Turaev TQFTs are fully extended? I know they've been extended down to dimension 1, and that it's believed that they can be fully extended to dimension 0, but I wasn't aware of a proof. (Of course, I could just be out of the loop.) $\endgroup$
    – Arun Debray
    Jan 16, 2018 at 17:35
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    $\begingroup$ Depends what you mean, do you want a 3210 theory for some delooping of categories, or for a particular delooping? $\endgroup$
    – Noah Snyder
    Jan 16, 2018 at 18:52
  • $\begingroup$ Thank you a lot. This is exactly what I was looking for. Sorry for the confusion. I was thinking about extenions down to dimenion 1 when I wrote "fully extended". This is missleading. $\endgroup$
    – BGJ
    Jan 17, 2018 at 13:23

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