On Strict Higher C*-categories
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866915589950275584 |
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| author | Bertozzini, Paolo Conti, Roberto Lewkeeratiyutkul, Wicharn Suthichitranont, Noppakhun |
| author_facet | Bertozzini, Paolo Conti, Roberto Lewkeeratiyutkul, Wicharn Suthichitranont, Noppakhun |
| contents | We provide definitions for strict involutive higher categories (a vertical categorification of dagger categories), strict higher C*-categories and higher Fell bundles (over arbitrary involutive higher topological categories). We put forward a proposal for a relaxed form of the exchange property for higher (C*)-categories that avoids the Eckmann-Hilton collapse and hence allows the construction of explicit non-trivial "non-commutative" examples arising from the study of hypermatrices and hyper-C*-algebras, here defined. Alternatives to the usual globular and cubical settings for strict higher categories are also explored. Applications of these non-commutative higher C*-categories are envisaged in the study of morphisms in non-commutative geometry and in the algebraic formulation of relational quantum theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_09339 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | On Strict Higher C*-categories Bertozzini, Paolo Conti, Roberto Lewkeeratiyutkul, Wicharn Suthichitranont, Noppakhun Operator Algebras Category Theory 18D05 (Primary) 46M15, 46M99, 16D90 (Secondary) We provide definitions for strict involutive higher categories (a vertical categorification of dagger categories), strict higher C*-categories and higher Fell bundles (over arbitrary involutive higher topological categories). We put forward a proposal for a relaxed form of the exchange property for higher (C*)-categories that avoids the Eckmann-Hilton collapse and hence allows the construction of explicit non-trivial "non-commutative" examples arising from the study of hypermatrices and hyper-C*-algebras, here defined. Alternatives to the usual globular and cubical settings for strict higher categories are also explored. Applications of these non-commutative higher C*-categories are envisaged in the study of morphisms in non-commutative geometry and in the algebraic formulation of relational quantum theory. |
| title | On Strict Higher C*-categories |
| topic | Operator Algebras Category Theory 18D05 (Primary) 46M15, 46M99, 16D90 (Secondary) |
| url | https://arxiv.org/abs/1709.09339 |