On the Axioms of Arboreal Categories
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908906944462848 |
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| author | Jakl, Tomáš Reggio, Luca |
| author_facet | Jakl, Tomáš Reggio, Luca |
| contents | Arboreal categories were introduced as an axiomatic framework for game comonads, which provide a comonadic view on many model-comparison games in logic. We demonstrate the inadequacy of the axiom stating that paths are connected. We then propose the notion of ``tree-connectedness'' to address this deficiency, and show that all the essential properties of arboreal categories that we are aware of remain valid under this new definition. Furthermore, we show that the path functor is a Street fibration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21841 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Axioms of Arboreal Categories Jakl, Tomáš Reggio, Luca Logic in Computer Science Category Theory Logic Arboreal categories were introduced as an axiomatic framework for game comonads, which provide a comonadic view on many model-comparison games in logic. We demonstrate the inadequacy of the axiom stating that paths are connected. We then propose the notion of ``tree-connectedness'' to address this deficiency, and show that all the essential properties of arboreal categories that we are aware of remain valid under this new definition. Furthermore, we show that the path functor is a Street fibration. |
| title | On the Axioms of Arboreal Categories |
| topic | Logic in Computer Science Category Theory Logic |
| url | https://arxiv.org/abs/2603.21841 |