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May 6, 2017 at 16:14 comment added Mike Shulman I'm pretty sure that stability is necessary. One good place to look for a counterexample would be $\mathcal{C}=\mathrm{Cat}$, cf ncatlab.org/nlab/show/double+profunctor
May 6, 2017 at 12:31 history edited twocubes CC BY-SA 3.0
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May 6, 2017 at 12:25 history edited Mike Shulman CC BY-SA 3.0
The question is about composing, not constructing
May 6, 2017 at 12:24 history edited twocubes CC BY-SA 3.0
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May 6, 2017 at 8:49 comment added Peter LeFanu Lumsdaine Like you, I can’t see how to do it without the extra stability assumption. I can’t see any way to formally back this up enough to justify a negative answer, though, so just commenting as a second opinion.
May 6, 2017 at 8:23 history asked twocubes CC BY-SA 3.0