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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.00995 |
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| _version_ | 1866911132046852096 |
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| author | Hungar, Brett |
| author_facet | Hungar, Brett |
| contents | Anchored planar algebras, a generalized notion of Vaughan Jones' planar algebras, have recently seen use in higher category theory, functional analysis, and TQFT applications. These algebras are equipped with a natural 3-dimensional graphical calculus. We compare this graphical calculus with the 3-dimensional graphical calculus associated to tricategories, and we show that anchored planar algebras can be thought of as living in a particular tricategory. This allows for more general techniques to be applied to anchored planar algebras and expands the types of diagrams that anchored planar algebras can interpret. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anchored Planar Algebras and 3-Categorical Graphical Calculus Hungar, Brett Category Theory Quantum Algebra 18M05, 18M30, 18M40, 18M65 Anchored planar algebras, a generalized notion of Vaughan Jones' planar algebras, have recently seen use in higher category theory, functional analysis, and TQFT applications. These algebras are equipped with a natural 3-dimensional graphical calculus. We compare this graphical calculus with the 3-dimensional graphical calculus associated to tricategories, and we show that anchored planar algebras can be thought of as living in a particular tricategory. This allows for more general techniques to be applied to anchored planar algebras and expands the types of diagrams that anchored planar algebras can interpret. |
| title | Anchored Planar Algebras and 3-Categorical Graphical Calculus |
| topic | Category Theory Quantum Algebra 18M05, 18M30, 18M40, 18M65 |
| url | https://arxiv.org/abs/2509.00995 |