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The universal coCartesian fibration

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arxiv 2210.08945 v1 pith:M2TBJPJH submitted 2022-10-17 math.CT math.ATmath.LO

Denis-Charles Cisinski , Hoang Kim Nguyen This is my paper · ORCID
classification math.CTmath.ATmath.LO
keywords cocartesianfibrationuniversalcorrespondencegeneralizationgiveproofproperty
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We give a new proof of the straightening/unstraightening correspondence by proving a generalization of the univalence property of the universal coCartesian fibration.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cosmological Unstraightening

    math.CT 2025-05 accept novelty 7.0 of 10

    The straightening-unstraightening equivalence between presheaves and fibrations lifts to a biequivalence of infinity-cosmoi for all models of (infinity,1)-categories.

  2. Synthetic perspectives on spaces and categories

    math.CT 2025-10 conditional novelty 3.0 of 10

    A well-referenced exposition of path and arrow induction plus (directed) univalent universes for synthetic spaces and categories, with small strengthened lemmas and a preview of directed univalence.

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