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Mar 15, 2016 at 23:35 comment added Jamie Vicary Say an object X has a weak dual when it satisfies the property at the top of your post. Then another funny aspect to this is that nobody seems to know a finite-dimensional semisimple k-linear tensor category with an object that has a weak dual, but not a dual.
Mar 15, 2016 at 22:12 history answered Qiaochu Yuan CC BY-SA 3.0