Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908349544529920 |
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| author | Kemp, Cameron James Deverall |
| author_facet | Kemp, Cameron James Deverall |
| contents | This paper follows on from ``Infinitesimal 2-braidings from 2-shifted Poisson structures". It is demonstrated that the hexagonators appearing at second order satisfy the requisite axioms of a braided monoidal cochain 2-category provided that the strict infinitesimal 2-braiding is totally symmetric and coherent (in Cirio and Faria Martins' sense). We show that those infinitesimal 2-braidings induced by 2-shifted Poisson structures are indeed totally symmetric and we relate coherency to the third-weight component of the Maurer-Cartan equation that a 2-shifted Poisson structure must satisfy. Furthermore, we show that 3-shifted Poisson structures and ``coboundary" 2-shifted Poisson structures induce syllepses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings Kemp, Cameron James Deverall Quantum Algebra Mathematical Physics Category Theory 14A30, 17B37, 18N10, 53D55 This paper follows on from ``Infinitesimal 2-braidings from 2-shifted Poisson structures". It is demonstrated that the hexagonators appearing at second order satisfy the requisite axioms of a braided monoidal cochain 2-category provided that the strict infinitesimal 2-braiding is totally symmetric and coherent (in Cirio and Faria Martins' sense). We show that those infinitesimal 2-braidings induced by 2-shifted Poisson structures are indeed totally symmetric and we relate coherency to the third-weight component of the Maurer-Cartan equation that a 2-shifted Poisson structure must satisfy. Furthermore, we show that 3-shifted Poisson structures and ``coboundary" 2-shifted Poisson structures induce syllepses. |
| title | Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings |
| topic | Quantum Algebra Mathematical Physics Category Theory 14A30, 17B37, 18N10, 53D55 |
| url | https://arxiv.org/abs/2505.01949 |