When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914774979182592 |
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| author | Bonchi, Filippo Di Giorgio, Alessandro Trotta, Davide |
| author_facet | Bonchi, Filippo Di Giorgio, Alessandro Trotta, Davide |
| contents | Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and complete. This paper illustrates a correspondence between fo-bicategories and Lawvere's hyperdoctrines. To streamline our proof, we introduce peircean bicategories, which offer a more succinct characterization of fo-bicategories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines Bonchi, Filippo Di Giorgio, Alessandro Trotta, Davide Category Theory Logic in Computer Science Fo-bicategories are a categorification of Peirce's calculus of relations. Notably, their laws provide a proof system for first-order logic that is both purely equational and complete. This paper illustrates a correspondence between fo-bicategories and Lawvere's hyperdoctrines. To streamline our proof, we introduce peircean bicategories, which offer a more succinct characterization of fo-bicategories. |
| title | When Lawvere meets Peirce: an equational presentation of boolean hyperdoctrines |
| topic | Category Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2404.18795 |