Cell 2-Representations for p-DG 2-categories

This is a report on joint work in progress with Vanessa Miemietz (UEA). This work adapts the theory of 2-representations which was developed in a series of papers by Mazorchuk–Miemietz to a setup enriched over graded vector spaces with a p-differential. This approach is motivated by the recent categorification of quantum sl_2 at prime roots of unity (Elias–Qi), using methods of Hopfological algebra (introduced by Khovanov–Qi). Under some technical assumptions, we can adapt the theory of cell 2-representations to this setup and relate to the categorification of simple modules over the small quantum group.