Classifying anima of condensed $\infty$-categories of points
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914349835091968 |
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| author | Haine, Peter J. |
| author_facet | Haine, Peter J. |
| contents | We compare the classifying anima of two natural condensed $\infty$-categories associated to a coherent $\infty$-topos. One from our work with Barwick and Glasman on exit-path categories in algebraic geometry, and the other from Lurie's work on ultracategories. The key consequence of our comparison is a connection between algebraic geometry and model theory: up to a mild completion, the proétale fundamental group of a scheme and the Lascar group of a complete first-order theory are both special cases of the same construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classifying anima of condensed $\infty$-categories of points Haine, Peter J. Category Theory Algebraic Topology We compare the classifying anima of two natural condensed $\infty$-categories associated to a coherent $\infty$-topos. One from our work with Barwick and Glasman on exit-path categories in algebraic geometry, and the other from Lurie's work on ultracategories. The key consequence of our comparison is a connection between algebraic geometry and model theory: up to a mild completion, the proétale fundamental group of a scheme and the Lascar group of a complete first-order theory are both special cases of the same construction. |
| title | Classifying anima of condensed $\infty$-categories of points |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2602.21330 |