(Pointed) Univalence in Universe Category Models of Type Theory (2512.16697v1)

Published 18 Dec 2025 in cs.LO, math.CT, and math.LO

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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