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Nov 19, 2018 at 19:30 comment added Keith Kearnes @BenEva: I don't know if there exist such $C$ and $D$.
Nov 15, 2018 at 12:21 comment added King Kong Fantastic, thanks, this is very helpful. As a small follow up, what are some interesting examples of equivalent but non-isomorphic categories $C$ and $D$ which do satisfy both (i) and (ii) for any $E$?
Nov 15, 2018 at 12:18 vote accept King Kong
Nov 11, 2018 at 16:32 history answered Keith Kearnes CC BY-SA 4.0