Deformation cohomology of tensor categories and extensions

Alexei Davydov – 14 December 2022

Deformation cohomology of tensor categories describe (first order) infinitesimal deformations of tensor categories, tensor functors and tensor natural transformations. In a recent paper Gainutdinov, Haferkamp and Schweigert showed that for a finite tensor category the deformation cohomology coincides with the self-extension groups in the monoidal centre. This fact can be used to prove vanishing of the deformation cohomology (Ocneanu rigidity) for fusion categories. In the talk I will report on the joint project with R. Street, which aims at extending the above results and provides other vanishing results for deformation cohomology.