Pretriangulated 2-representations via dg algebra 1-morphisms

Laugwitz, Robert; Miemietz, Vanessa

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.

Citation

Laugwitz, R., & Miemietz, V. (in press). Pretriangulated 2-representations via dg algebra 1-morphisms. Documenta Mathematica,

• Journal Article Type: Article
• Acceptance Date: Apr 14, 2025
• Deposit Date: Apr 25, 2025
• Publicly Available Date: Apr 25, 2025
• Journal: Documenta Mathematica
• Print ISSN: 1431-0635
• Electronic ISSN: 1431-0643
• Publisher: EMS Press
• Peer Reviewed: Peer Reviewed
• Keywords: 2-category, 2-representation, differential graded category, pretriangulated category, homotopy category.
• Public URL: https://nottingham-repository.worktribe.com/output/48097190
• Publisher URL: https://ems.press/journals/dm