Non-semisimple extended TQFTs

In 2014 Costantino, Geer and Patureau (CGP for short) defined a family of non-semisimple Witten-Reshetikhin-Turaev-type invariants of 3-manifolds. The main ingredient for their construction is a certain class of ribbon categories, called relative pre-modular categories, which are modeled on complex-weight representations of the so-called "unrolled" version of quantum sl(2) at a root of unity, and which are not required to be semisimple. We find conditions for these relative 

pre-modular categories under which the CGP invariants can be extended to graded ETQFTs. Our construction agrees with the recent result by Blanchet, Costantino, Geer and Patureau which provides a Z-graded TQFT extension for the CGP invariants in the special case of unrolled quantum sl(2).