Hopfological algebra, revisited

This talk is based on joint work with Omar Gómez (Bielefeld) and Marius Nielsen (NTNU). Hopfological algebra is a variant of classical homological algebra introduced by Khovanov and Qi, motivated by potential applications in the categorification of quantum invariants of 3-manifolds. In this talk, I will explain an infinity-categorical approach to the theory that leads, in particular, to refined foundations as well as to "hopfological analogues" of classical invariants such as Hochschild (co)homology.