Higher Witt Groups for 2-Categories I: Centralizers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910876241494016 |
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| author | Xu, Hao |
| author_facet | Xu, Hao |
| contents | In this article, we investigate monoidal, braided, sylleptic centralizers of monoidal, braided, sylleptic 2-functors. We specifically focus on multifusion 2-categories and show that monoidal, braided, sylleptic centralizers are multifusion again, via studying the corresponding enveloping algebras. We provide a characterization of the non-degeneracy condition for monoidal, braided, and sylleptic fusion 2-categories, via vanishing of their centers. Applying Double Centralizer Theorems, we establish the relationship between monoidal, braided, symmetric local modules and free modules. In particular, we obtain factorization properties of non-degenerate monoidal, braided, and sylleptic fusion 2-categories. Main results in this article will be used to study higher Witt equivalences of non-degenerate monoidal, braided, sylleptic 2-categories in the sequential articles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_07768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Witt Groups for 2-Categories I: Centralizers Xu, Hao Category Theory 18M20, 18N10, 18N25 In this article, we investigate monoidal, braided, sylleptic centralizers of monoidal, braided, sylleptic 2-functors. We specifically focus on multifusion 2-categories and show that monoidal, braided, sylleptic centralizers are multifusion again, via studying the corresponding enveloping algebras. We provide a characterization of the non-degeneracy condition for monoidal, braided, and sylleptic fusion 2-categories, via vanishing of their centers. Applying Double Centralizer Theorems, we establish the relationship between monoidal, braided, symmetric local modules and free modules. In particular, we obtain factorization properties of non-degenerate monoidal, braided, and sylleptic fusion 2-categories. Main results in this article will be used to study higher Witt equivalences of non-degenerate monoidal, braided, sylleptic 2-categories in the sequential articles. |
| title | Higher Witt Groups for 2-Categories I: Centralizers |
| topic | Category Theory 18M20, 18N10, 18N25 |
| url | https://arxiv.org/abs/2403.07768 |