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I understand that you are copying material, but let’s do a minimum of adjustment so that it makes sense in the larger context of the nLab.
If you point to the nLab’s entry category then it’s hard for the reader to understand what kind of completion you have in mind. Better to point more specifically to internal category in homotopy type theory – at least for the first occasion.
I am taking the liberty of adding to the References-section the following:
The relation between Segal completeness (now often “Rezk completion”) for internal categories in HoTT and the univalence axiom had been pointed out in:
I have completed the publication data for:
By the way, if you list items (such as under “See also”) without a bullet or numbering in front, then the the parser thinks you keep starting new paragraphs for each item and produces overly large vertical whitespace. Best to use bullet lists markup like this:
* an item
* another
* yet another
I have changed the Theorem from a subsection to a theorem-environment (now here), analogously for the proof. Notice the easily remembered code:
\begin{theorem}...\end{theorem} \begin{proof} ... \end{proof}
By the way, after the proof ends, the text keeps going in a surprising/unclear way. Maybe there is some guiding text missing and/or the proof doesn’t actually end at that point.
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