Homotopy type theory as a language for diagrams of $\infty$-logoses
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912969692020736 |
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| author | Uemura, Taichi |
| author_facet | Uemura, Taichi |
| contents | We show that certain diagrams of $\infty$-logoses are reconstructed in homotopy type theory extended with some lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single $\infty$-logos but also a diagram of $\infty$-logoses. This also provides a higher dimensional version of Sterling's synthetic Tait computability -- a type theory for higher dimensional logical relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_02444 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homotopy type theory as a language for diagrams of $\infty$-logoses Uemura, Taichi Category Theory Logic in Computer Science Logic We show that certain diagrams of $\infty$-logoses are reconstructed in homotopy type theory extended with some lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single $\infty$-logos but also a diagram of $\infty$-logoses. This also provides a higher dimensional version of Sterling's synthetic Tait computability -- a type theory for higher dimensional logical relations. |
| title | Homotopy type theory as a language for diagrams of $\infty$-logoses |
| topic | Category Theory Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2212.02444 |