The straightening-unstraightening equivalence between presheaves and fibrations lifts to a biequivalence of infinity-cosmoi for all models of (infinity,1)-categories.
The universal coCartesian fibration
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abstract
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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math.CT 1years
2025 1verdicts
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Cosmological Unstraightening
The straightening-unstraightening equivalence between presheaves and fibrations lifts to a biequivalence of infinity-cosmoi for all models of (infinity,1)-categories.