Pretriangulated 2-representations via dg algebra 1-morphisms
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909589054685184 |
|---|---|
| author | Laugwitz, Robert Miemietz, Vanessa |
| author_facet | Laugwitz, Robert Miemietz, Vanessa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09999 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pretriangulated 2-representations via dg algebra 1-morphisms Laugwitz, Robert Miemietz, Vanessa Representation Theory Category Theory Quantum Algebra 18N10, 18N25, 16E45 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. |
| title | Pretriangulated 2-representations via dg algebra 1-morphisms |
| topic | Representation Theory Category Theory Quantum Algebra 18N10, 18N25, 16E45 |
| url | https://arxiv.org/abs/2205.09999 |