(Pointed) Univalence in Universe Category Models of Type Theory

Chris Kapulkin; Yufeng Li

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arXiv · 2512.16697

(Pointed) Univalence in Universe Category Models of Type Theory

Chris Kapulkin·Yufeng Li

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Abstract

We provide a formulation of the univalence axiom in a universe category model of dependent type theory that is convenient to verify in homotopy-theoretic settings. We further develop a strengthening of the univalence axiom, called pointed univalence, that is both computationally desirable and semantically natural, and verify its closure under Artin-Wraith gluing and formation of inverse diagrams.

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Chris Kapulkin, Yufeng Li. 2025-12-18. (Pointed) Univalence in Universe Category Models of Type Theory. https://arxiv.org/abs/2512.16697

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