Timeline for What is the category of covariant and contravariant functors?
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| Apr 3, 2021 at 18:42 | comment | added | Mike Shulman | Yes, I expect it should have some limits and colimits as an enriched category. At least, conical ones, as well as the copowers I mentioned (which are also powers, since the object in question is dualizable). I doubt that it is complete and cocomplete as an enriched category, though: there are so many weird objects of $\bf Cat \times Cat$ that it seems unlikely $\bf Cat'$ would have powers and copowers by them all. | |
| Apr 3, 2021 at 16:57 | comment | added | Claudio Pisani | maybe, as suggested by Simon, that your approach gives some hints on the completeness of $\bf Cat'$? (see the comments above) | |
| Apr 2, 2021 at 15:26 | history | answered | Mike Shulman | CC BY-SA 4.0 |