Adding a constant and an axiom to a doctrine
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913554958909440 |
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| author | Guffanti, Francesca |
| author_facet | Guffanti, Francesca |
| contents | We study the meaning of "adding a constant to a language" for any doctrine, and "adding an axiom to a theory" for a primary doctrine, by showing how these are actually two instances of the same construction. We prove their universal properties, and how these constructions are compatible with additional structure on the doctrine. Existence of Kleisli object for comonads in the 2-category of indexed poset is proved in order to build these constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08324 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Adding a constant and an axiom to a doctrine Guffanti, Francesca Category Theory Logic We study the meaning of "adding a constant to a language" for any doctrine, and "adding an axiom to a theory" for a primary doctrine, by showing how these are actually two instances of the same construction. We prove their universal properties, and how these constructions are compatible with additional structure on the doctrine. Existence of Kleisli object for comonads in the 2-category of indexed poset is proved in order to build these constructions. |
| title | Adding a constant and an axiom to a doctrine |
| topic | Category Theory Logic |
| url | https://arxiv.org/abs/2310.08324 |