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Mar 15, 2016 at 22:12 answer added Qiaochu Yuan timeline score: 4
Mar 13, 2016 at 8:41 comment added Jamie Vicary Hi Todd, no, I don't assume anything more than specified in the question. If all objects have duals then this implies this good interaction between the semiadditive structure and the monoidal product - this is what I was alluding to in the question.
Mar 13, 2016 at 1:36 comment added Todd Trimble So I guess you know that categories with biproducts are canonically enriched in commutative monoids. Do you also assume the compatibility between the monoidal structure and the biproducts that would say the monoidal product as a functor is enriched in commutative monoids? I believe the answer would have to be 'yes' in that case, but would be skeptical otherwise.
Mar 13, 2016 at 0:17 history asked Jamie Vicary CC BY-SA 3.0