Categorical univalence of a universe does not entail function extensionality, as shown by polynomial models of type theory that refute the latter while satisfying the former.
L.,Groupoidal realizability for intensional type theory, Mathematical Structures in Computer Science34, pages 911–944 (2024)
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Univalence without function extensionality
Categorical univalence of a universe does not entail function extensionality, as shown by polynomial models of type theory that refute the latter while satisfying the former.