Generalized Witt and Morita equivalences
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909887099830272 |
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| author | Kong, Liang Wang, Yilong Zheng, Hao |
| author_facet | Kong, Liang Wang, Yilong Zheng, Hao |
| contents | In this work, we introduce a family of new equivalence relations among fusion categories that are less refined than the usual Morita equivalence. We obtain abelian groups by quotienting these new equivalence relations from the commutative monoids of the equivalence classes of all fusion categories. Moreover, we upgrade them to equivalence relations among nondegenerate braided fusion categories that are more refined than the usual Witt equivalence. As a consequence, we obtain new abelian groups that are more refined than the usual Witt group. These new groups allow us to access the internal structures within Witt classes. We expect that they are useful in the classification program of (braided) fusion (higher) categories and in the study of gapless edges of 2+1D topological orders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Witt and Morita equivalences Kong, Liang Wang, Yilong Zheng, Hao Quantum Algebra Strongly Correlated Electrons High Energy Physics - Theory Category Theory In this work, we introduce a family of new equivalence relations among fusion categories that are less refined than the usual Morita equivalence. We obtain abelian groups by quotienting these new equivalence relations from the commutative monoids of the equivalence classes of all fusion categories. Moreover, we upgrade them to equivalence relations among nondegenerate braided fusion categories that are more refined than the usual Witt equivalence. As a consequence, we obtain new abelian groups that are more refined than the usual Witt group. These new groups allow us to access the internal structures within Witt classes. We expect that they are useful in the classification program of (braided) fusion (higher) categories and in the study of gapless edges of 2+1D topological orders. |
| title | Generalized Witt and Morita equivalences |
| topic | Quantum Algebra Strongly Correlated Electrons High Energy Physics - Theory Category Theory |
| url | https://arxiv.org/abs/2511.02624 |