2022/05/20 by Robert Laugwitz, Laugwitz, Robert, Vanessa Miemietz +1
Mathematics · #16E45 #18N10 #18N25 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2205.09999
openalex publication_date 2022/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.