Equivalent definitions of fusion category arising from separability
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911435202756608 |
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| author | Zuo, Zhenbang |
| author_facet | Zuo, Zhenbang |
| contents | For a semisimple multiring category with left duals, we prove that the unit object is simple if and only if the tensor functors by any non-zero algebra are separable (resp. faithful, resp. Maschke, resp. dual Maschke, resp. conservative). This induces a list of equivalent definitions of fusion category. As an application, we describe the connectness of a class of weak Hopf algebras by the separability of tensor functors. We also consider applications to transfer of simplicity between the unit objects, semisimple indecomposable module category and Grothendieck ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivalent definitions of fusion category arising from separability Zuo, Zhenbang Category Theory Primary 18M20, Secondary 18A22 For a semisimple multiring category with left duals, we prove that the unit object is simple if and only if the tensor functors by any non-zero algebra are separable (resp. faithful, resp. Maschke, resp. dual Maschke, resp. conservative). This induces a list of equivalent definitions of fusion category. As an application, we describe the connectness of a class of weak Hopf algebras by the separability of tensor functors. We also consider applications to transfer of simplicity between the unit objects, semisimple indecomposable module category and Grothendieck ring. |
| title | Equivalent definitions of fusion category arising from separability |
| topic | Category Theory Primary 18M20, Secondary 18A22 |
| url | https://arxiv.org/abs/2602.08954 |