Pretriangulated 2-representations via dg algebra 1-morphisms

Laugwitz, Robert and Miemietz, Vanessa (2025) Pretriangulated 2-representations via dg algebra 1-morphisms. Documenta Mathematica, 30 (6). 1271–1323. ISSN 1431-0643

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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.

Item Type:	Article
Additional Information:	Funding: V. Miemietz was supported by EPSRC grant EP/S017216/1 and R. Laugwitz was supported by a Nottingham Research Fellowship
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	LivePure Connector
Date Deposited:	25 Apr 2025 16:30
Last Modified:	11 Oct 2025 10:08
URI:	https://ueaeprints.uea.ac.uk/id/eprint/99096
DOI:	10.4171/DM/1029

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