| Résume | Recent work of Costantino, Geer and Patureau provides the general theory for the construction of non-semisimple Witten-Reshetikhin-Turaev-type invariants of closed 3-manifolds. The main ingredient for their recipe is a certain class of non-semisimple 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 roots of unity. We generalize this construction by finding conditions for these relative pre-modular categories under which the Costantino-Geer-Patureau invariants can be extended to ETQFTs. In particular our result produces a new family of non-semisimple ETQFTs extending the non-semisimple TQFTs constructed by Blanchet, Costantino, Geer and Patureau in the special case of unrolled quantum sl(2).
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