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Is there a way in which Conduche fibrations can lead to completeness in double categories? I know that Conduche conditions on functors play a role in completeness or cocompleteness in pseudo-double categories (see http://www.numdam.org/article/CTGDC_2007__48_3_163_0.pdf)

Are there papers in which this idea is explored? (Struggling to find them!) Ayala has looked at this for $\infty-$categories.

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  • $\begingroup$ I have provided the link on the paper that discussed this on weak double categories. $\endgroup$
    – Siya
    Commented May 3 at 7:53
  • $\begingroup$ How is your question not addressed by the paper you link? $\endgroup$
    – Kevin Carlson
    Commented May 7 at 4:09

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