Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866912194798551040 |
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| author | Raynor, Sophie |
| author_facet | Raynor, Sophie |
| contents | Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of Jones's planar algebras. They are very closely related to circuit operads, which are a variation of modular operads admitting an extra monoidal product. This paper gives a description of circuit algebras in terms categories of Brauer diagrams. An abstract nerve theorem for circuit operads -- and hence circuit algebras -- is proved using an iterated distributive law, and an existing nerve theorem for modular operads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_04557 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras Raynor, Sophie Category Theory 18M85 (Primary) 18M10, 57K12 (Secondary) Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of Jones's planar algebras. They are very closely related to circuit operads, which are a variation of modular operads admitting an extra monoidal product. This paper gives a description of circuit algebras in terms categories of Brauer diagrams. An abstract nerve theorem for circuit operads -- and hence circuit algebras -- is proved using an iterated distributive law, and an existing nerve theorem for modular operads. |
| title | Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras |
| topic | Category Theory 18M85 (Primary) 18M10, 57K12 (Secondary) |
| url | https://arxiv.org/abs/2108.04557 |