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Tarski universes are supposed to refer to the entire structure consisting of a type $U$ and the type family $El$, not just the type $U$. So the corresponding name should be “univalent type with a type family” rather than “univalent index type of a type family”.
Renamed due to parallels with other univalent objects like univalent category and univalent universe
Anonymous
expanded article significantly and renamed article to Tarski universe; the whole reason why one would want such an object is to build up various notions of Tarski universes in type theory, which may or may not be strictly or weakly closed under various type formers in the type theory
Anonymous
added what I guess is the original reference:
and expanded out this bibitem:
The entry used to point the reader to section 2.1.6 in there. But at least the above pdf version has no such section, instead the section titled “Universes” is 2.3.5. So I changed this, but let me know if I am missing something.
added pointer to:
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