Lurie's Unstraightening as a weak biequivalence of $\infty$-cosmoses
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916145128275968 |
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| author | Stenzel, Raffael |
| author_facet | Stenzel, Raffael |
| contents | We give a direct proof of the fact that Lurie's Unstraightening functor induces an equivalence between the strict $(\infty,2)$-category of indexed quasi-categories and the strict $(\infty,2)$-category of fibered quasi-categories over any given quasi-categorical base. We conclude that Unstraightening preserves simplicial cotensors up to a (strictly) natural homotopy equivalence, and thus gives rise to an accordingly weakened notion of cosmological biequivalence between the two underlying $\infty$-cosmoses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lurie's Unstraightening as a weak biequivalence of $\infty$-cosmoses Stenzel, Raffael Category Theory We give a direct proof of the fact that Lurie's Unstraightening functor induces an equivalence between the strict $(\infty,2)$-category of indexed quasi-categories and the strict $(\infty,2)$-category of fibered quasi-categories over any given quasi-categorical base. We conclude that Unstraightening preserves simplicial cotensors up to a (strictly) natural homotopy equivalence, and thus gives rise to an accordingly weakened notion of cosmological biequivalence between the two underlying $\infty$-cosmoses. |
| title | Lurie's Unstraightening as a weak biequivalence of $\infty$-cosmoses |
| topic | Category Theory |
| url | https://arxiv.org/abs/2403.01167 |