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arXiv · 2205.09999

Pretriangulated 2-representations via dg algebra 1-morphisms

Robert Laugwitz·Vanessa Miemietz
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Abstract

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

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BibTeXRIS

Robert Laugwitz, Vanessa Miemietz. 2022-05-20. Pretriangulated 2-representations via dg algebra 1-morphisms. https://arxiv.org/abs/2205.09999

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