A synthetic construction of universal cocartesian fibrations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914431902941184 |
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| author | Sattler, Christian Wärn, David |
| author_facet | Sattler, Christian Wärn, David |
| contents | We give a model-independent construction of directed univalent cocartesian fibrations of $(\infty,1)$-categories, and prove a straightening equivalence against such fibrations. The key step is showing that cocartesian fibrations descend along localisations, which we accomplish by analysing mapping spaces of localisations. Along the way we introduce a directed version of the join construction, giving a sequential colimit description of the full image of any functor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A synthetic construction of universal cocartesian fibrations Sattler, Christian Wärn, David Category Theory Algebraic Topology We give a model-independent construction of directed univalent cocartesian fibrations of $(\infty,1)$-categories, and prove a straightening equivalence against such fibrations. The key step is showing that cocartesian fibrations descend along localisations, which we accomplish by analysing mapping spaces of localisations. Along the way we introduce a directed version of the join construction, giving a sequential colimit description of the full image of any functor. |
| title | A synthetic construction of universal cocartesian fibrations |
| topic | Category Theory Algebraic Topology |
| url | https://arxiv.org/abs/2603.28688 |