Work

Pretriangulated 2-representations via dg algebra 1-morphisms

Year: 2025

Type: article

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.

Source: Documenta Mathematica

DOI: 10.4171/dm/1029

Authors: Robert Laugwitz, Vanessa Miemietz

Institutions: University of Nottingham, University of East Anglia

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Engineering and Physical Sciences Research Council

Awards: 2-representation theory and categorification, G8178268023