# Pretriangulated 2-representations via dg algebra 1-morphisms

@inproceedings{Laugwitz2022Pretriangulated2V, title={Pretriangulated 2-representations via dg algebra 1-morphisms}, author={Robert Laugwitz and Vanessa Miemietz}, year={2022} }

. This paper develops a theory of pretriangulated 2 -representations of dg 2 -categories. We characterize cyclic pretriangulated 2 -representations, un- der certain compactness assumptions, in terms of modules over dg algebra 1 morphisms internal to associated dg 2 -categories of compact dg modules. Fur- ther, we investigate the Morita theory and quasi-equivalences for such dg 2 representations. We relate this theory to various classes of examples of dg cate- goriﬁcations from the literature.

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