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Pretriangulated 2-representations via dg algebra 1-morphisms

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arxiv 2205.09999 v2 pith:5H5LRBVA submitted 2022-05-20 math.RT math.CTmath.QA

Robert Laugwitz , Vanessa Miemietz This is my paper · ORCID
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keywords representationspretriangulatedtheoryalgebracategoriesmorphismsassociatedassumptions
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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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  1. Induction for extended affine type A Soergel bimodules: first steps

    math.RT 2025-07 accept novelty 6.0 of 10

    A categorical embedding Ψ for extended affine type A Soergel bimodules is constructed, categorifying the Hecke algebra parabolic embedding, with an example categorifying the Zelevinsky tensor product of two trivial re...

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