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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.01167 |
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Table of 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.