Foundations for operator algebraic tricategories
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914744159436800 |
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| author | Ferrer, Giovanni |
| author_facet | Ferrer, Giovanni |
| contents | An operator algebraic tricategory is a higher categorical analogue of an operator algebra. For algebraic tricategories, Gordon, Power, and Street proved that every algebraic tricategory is equivalent to a Gray-category, a result later refined by Gurski. We adapt this result to the context of functional analysis, showing that every operator algebraic tricategory is equivalent to an operator Gray-category. We then categorify the Gelfand-Naimark theorem for operator algebras, inductively proving that every (small) operator algebraic tricategory is equivalent to a concrete operator Gray-category. We also provide several examples of interest for operator algebraic tricategories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Foundations for operator algebraic tricategories Ferrer, Giovanni Operator Algebras Category Theory Functional Analysis Quantum Algebra 46M15 18N20 18M40 An operator algebraic tricategory is a higher categorical analogue of an operator algebra. For algebraic tricategories, Gordon, Power, and Street proved that every algebraic tricategory is equivalent to a Gray-category, a result later refined by Gurski. We adapt this result to the context of functional analysis, showing that every operator algebraic tricategory is equivalent to an operator Gray-category. We then categorify the Gelfand-Naimark theorem for operator algebras, inductively proving that every (small) operator algebraic tricategory is equivalent to a concrete operator Gray-category. We also provide several examples of interest for operator algebraic tricategories. |
| title | Foundations for operator algebraic tricategories |
| topic | Operator Algebras Category Theory Functional Analysis Quantum Algebra 46M15 18N20 18M40 |
| url | https://arxiv.org/abs/2404.05193 |