Classification of generic quantum-group category deformations

Classify the pivotal infinitesimal deformations of quantum-group categories at generic quantum parameter, for example by computing their Davydov–Yetter cohomology.

Background

The paper classifies infinitesimal deformations of the quantum $G_2$ category and of the ribbon category associated with Deligne’s $S_t$. It notes that a broader classification for quantum-group categories at generic quantum parameter is not currently available in the literature. The authors indicate that computing Davydov–Yetter cohomology may provide a route to resolving this problem, but they do not carry out that analysis in the paper.