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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27466 |
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| _version_ | 1866915970521497600 |
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| author | de Brecht, Matthew |
| author_facet | de Brecht, Matthew |
| contents | An étale space over a topological space $Y$ is defined as a local homeomorphism from a topological space $X$ into $Y$. They often come up in topos theory because of the equivalence between sheaves and étale spaces over a space. In this note, we define computable étale spaces over a computable topological space $Y$ within the TTE framework of computable topology, and show they are naturally equivalent to computable functions from $Y$ to $\mathsf{ODS}$, the effective quasi-Polish category of overt-discrete quasi-Polish spaces. More generally, if $\cal C$ is a computable category (or groupoid), then there is an equivalence between computable functors from $\cal C$ to $\mathsf{ODS}$, and computable étale spaces equipped with a computable action by $\cal C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27466 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on computable étale spaces de Brecht, Matthew Logic Category Theory An étale space over a topological space $Y$ is defined as a local homeomorphism from a topological space $X$ into $Y$. They often come up in topos theory because of the equivalence between sheaves and étale spaces over a space. In this note, we define computable étale spaces over a computable topological space $Y$ within the TTE framework of computable topology, and show they are naturally equivalent to computable functions from $Y$ to $\mathsf{ODS}$, the effective quasi-Polish category of overt-discrete quasi-Polish spaces. More generally, if $\cal C$ is a computable category (or groupoid), then there is an equivalence between computable functors from $\cal C$ to $\mathsf{ODS}$, and computable étale spaces equipped with a computable action by $\cal C$. |
| title | A note on computable étale spaces |
| topic | Logic Category Theory |
| url | https://arxiv.org/abs/2604.27466 |