algebra / Tensor categories
Twisted Deligne products categorify the tensor product of two Grothendieck rings. Classifying them leads to categorical $n$-cocycles, and Johnson-Freyd, Ostrik and Yu asked whether these are always pullbacks of ordinary group cocycles on the universal grading group of the underlying based ring. For $3$-cocycles they are.
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Append-only history
answered for 3-cocycles, inside a broader partial classification of twisted Deligne products
Research memory
Twisted Deligne products categorify the tensor product of two Grothendieck rings. Classifying them leads to categorical $n$-cocycles, and Johnson-Freyd, Ostrik and Yu asked whether these are always pullbacks of ordinary group cocycles on the universal grading group of the underlying based ring. For $3$-cocycles they are.
answered for 3-cocycles, inside a broader partial classification of twisted Deligne products
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