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Jun 4, 2021 at 3:01 history became hot network question
Jun 3, 2021 at 22:27 comment added Martin Brandenburg (2) is the "correct" defintion. Equivalences are defined in any 2-category, and we just apply it to the special example of the (strict) 2-category of tensor categories. (1) is not the "correct" definition, it is a characterization, or actually a theorem (using (2) as a definition) that the forgetful 2-functor from tensor categories to categories is 2-conservative - a categorification of the statement that the forgetful functor from monoids to sets is conservative.
Jun 3, 2021 at 19:48 vote accept Andromeda
Jun 3, 2021 at 19:17 answer added Mike Shulman timeline score: 7
Jun 3, 2021 at 19:00 history asked Andromeda CC BY-SA 4.0