Non-trivial higher homotopy of first-order theories
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914984332623872 |
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| author | Campion, Tim Ye, Jinhe |
| author_facet | Campion, Tim Ye, Jinhe |
| contents | Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular, $π_2(\lvert\mathsf{Mod}(T)\rvert)=\mathbb{Z}$, which answers a question in our previous work. The computation is based on Connes' cycle category $Λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-trivial higher homotopy of first-order theories Campion, Tim Ye, Jinhe Logic Algebraic Topology Category Theory Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular, $π_2(\lvert\mathsf{Mod}(T)\rvert)=\mathbb{Z}$, which answers a question in our previous work. The computation is based on Connes' cycle category $Λ$. |
| title | Non-trivial higher homotopy of first-order theories |
| topic | Logic Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2306.12011 |