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.
K.,The Dialectica Models of Type Theory, Ph.D
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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.