A synthetic construction of universal cocartesian fibrations
Category Theory
2026-03-31 v1 Algebraic Topology
Abstract
We give a model-independent construction of directed univalent cocartesian fibrations of -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.
Keywords
Cite
@article{arxiv.2603.28688,
title = {A synthetic construction of universal cocartesian fibrations},
author = {Christian Sattler and David Wärn},
journal= {arXiv preprint arXiv:2603.28688},
year = {2026}
}
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31 pages