Finitary birepresentations of finitary bicategories
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866918532780916736 |
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| author | Mackaay, Marco Mazorchuk, Volodymyr Miemietz, Vanessa Tubbenhauer, Daniel Zhang, Xiaoting |
| author_facet | Mackaay, Marco Mazorchuk, Volodymyr Miemietz, Vanessa Tubbenhauer, Daniel Zhang, Xiaoting |
| contents | In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple transitive $2$-representations of a given $2$-category was reduced to that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes of $2$-representations. In this paper, we generalize them to biequivalences between certain $2$-categories of birepresentations. Furthermore, we prove an analog of the double centralizer theorem in finitary birepresentation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_01658 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Finitary birepresentations of finitary bicategories Mackaay, Marco Mazorchuk, Volodymyr Miemietz, Vanessa Tubbenhauer, Daniel Zhang, Xiaoting Representation Theory Category Theory In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple transitive $2$-representations of a given $2$-category was reduced to that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes of $2$-representations. In this paper, we generalize them to biequivalences between certain $2$-categories of birepresentations. Furthermore, we prove an analog of the double centralizer theorem in finitary birepresentation theory. |
| title | Finitary birepresentations of finitary bicategories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2008.01658 |