Generalised Orbifolds and G-equivariantisation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916787175555072 |
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| author | Heinrich, Sebastian Plavnik, Julia Runkel, Ingo Watkins, Abigail |
| author_facet | Heinrich, Sebastian Plavnik, Julia Runkel, Ingo Watkins, Abigail |
| contents | In a construction motivated by topological field theory, a so-called orbifold datum $\mathbb{A}$ in a ribbon category $C$ allows one to define a new ribbon category $C_{\mathbb{A}}$. If $C$ is the neutral component of a $G$-crossed ribbon category $B$, and $\mathbb{A}$ is an orbifold datum in $C$ defined in terms of $B$, one finds that $C_{\mathbb{A}}$ is equivalent to the equivariantisation $B^G$ of $B$ as a ribbon category. We give a constructive proof of this equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalised Orbifolds and G-equivariantisation Heinrich, Sebastian Plavnik, Julia Runkel, Ingo Watkins, Abigail Quantum Algebra High Energy Physics - Theory Category Theory In a construction motivated by topological field theory, a so-called orbifold datum $\mathbb{A}$ in a ribbon category $C$ allows one to define a new ribbon category $C_{\mathbb{A}}$. If $C$ is the neutral component of a $G$-crossed ribbon category $B$, and $\mathbb{A}$ is an orbifold datum in $C$ defined in terms of $B$, one finds that $C_{\mathbb{A}}$ is equivalent to the equivariantisation $B^G$ of $B$ as a ribbon category. We give a constructive proof of this equivalence. |
| title | Generalised Orbifolds and G-equivariantisation |
| topic | Quantum Algebra High Energy Physics - Theory Category Theory |
| url | https://arxiv.org/abs/2506.08154 |