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Nov 4, 2022 at 23:47 comment added Doron Grossman-Naples @Z.M True, but I think that this is just evidence that the p-complete category is itself problematic. I'm satisfied with the explanation that this is due to the fact that p-completion is not smashing.
Nov 4, 2022 at 20:25 comment added Z. M But you are interested in examples such as the category of p-complete objects, right? In this case, the unit is not compact.
Nov 4, 2022 at 19:27 vote accept Doron Grossman-Naples
Nov 4, 2022 at 19:26 comment added Doron Grossman-Naples @Z.M they may not in general, but they do in the case of interest; namely, the case where C is generated by a small set of compact rigid objects.
Nov 4, 2022 at 5:29 comment added Z. M What do you mean by thick primes in compact objects? Compact objects might not span a symmetric monoidal full subcategory.
Nov 3, 2022 at 22:29 history answered Doron Grossman-Naples CC BY-SA 4.0