A 3-categorical perspective on G-crossed braided categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866912909920043008 |
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| author | Jones, Corey Penneys, David Reutter, David |
| author_facet | Jones, Corey Penneys, David Reutter, David |
| contents | A braided monoidal category may be considered a $3$-category with one object and one $1$-morphism. In this paper, we show that, more generally, $3$-categories with one object and $1$-morphisms given by elements of a group $G$ correspond to $G$-crossed braided categories, certain mathematical structures which have emerged as important invariants of low-dimensional quantum field theories. More precisely, we show that the 4-category of $3$-categories $\mathcal{C}$ equipped with a 3-functor $\mathrm{B}G \to \mathcal{C}$ which is essentially surjective on objects and $1$-morphisms is equivalent to the $2$-category of $G$-crossed braided categories. This provides a uniform approach to various constructions of $G$-crossed braided categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_00405 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A 3-categorical perspective on G-crossed braided categories Jones, Corey Penneys, David Reutter, David Category Theory Quantum Algebra 18N20 (Primary), 18M30, 18M15 (Secondary) A braided monoidal category may be considered a $3$-category with one object and one $1$-morphism. In this paper, we show that, more generally, $3$-categories with one object and $1$-morphisms given by elements of a group $G$ correspond to $G$-crossed braided categories, certain mathematical structures which have emerged as important invariants of low-dimensional quantum field theories. More precisely, we show that the 4-category of $3$-categories $\mathcal{C}$ equipped with a 3-functor $\mathrm{B}G \to \mathcal{C}$ which is essentially surjective on objects and $1$-morphisms is equivalent to the $2$-category of $G$-crossed braided categories. This provides a uniform approach to various constructions of $G$-crossed braided categories. |
| title | A 3-categorical perspective on G-crossed braided categories |
| topic | Category Theory Quantum Algebra 18N20 (Primary), 18M30, 18M15 (Secondary) |
| url | https://arxiv.org/abs/2009.00405 |