A synthetic construction of universal cocartesian fibrations
Abstract
We give a model-independent construction of directed univalent cocartesian fibrations of (∞,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.
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