Monoidal bicategories, differential linear logic, and analytic functors
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908540240658432 |
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| author | Fiore, M. Gambino, N. Hyland, M. |
| author_facet | Fiore, M. Gambino, N. Hyland, M. |
| contents | We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation, introduced to study differential linear logic via differential categories. As an application, we extend the differential calculus of Joyal's analytic functors to analytic functors between presheaf categories, just as ordinary calculus extends from a single variable to many variables. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monoidal bicategories, differential linear logic, and analytic functors Fiore, M. Gambino, N. Hyland, M. Category Theory Logic in Computer Science Logic 18N10, 18M45, 18F40, 18D60, 18M80 We develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation, introduced to study differential linear logic via differential categories. As an application, we extend the differential calculus of Joyal's analytic functors to analytic functors between presheaf categories, just as ordinary calculus extends from a single variable to many variables. |
| title | Monoidal bicategories, differential linear logic, and analytic functors |
| topic | Category Theory Logic in Computer Science Logic 18N10, 18M45, 18F40, 18D60, 18M80 |
| url | https://arxiv.org/abs/2405.05774 |