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Nov 28, 2020 at 19:21 comment added Alec Rhea @MikeShulman Thank you for the correction.
Nov 28, 2020 at 17:16 comment added Mike Shulman Note that the adjective "discrete" is more commonly used for categories that have only identity $k$-cells for all $k>0$. Your "discrete bicategories" would more commonly be called something like "1-truncated".
Nov 28, 2020 at 15:48 comment added Alec Rhea @DavidRoberts Interesting, thank you for the reference, I'll have a look.
Nov 28, 2020 at 15:43 vote accept Alec Rhea
Nov 28, 2020 at 13:11 comment added David Roberts Going up a dimension there are sesquicategories, and: "A Gray-category does not have an underlying strict 2-category, but it does have an underlying strict sesquicategory." This seems to answer your last paragraph to some extent.
Nov 28, 2020 at 8:51 answer added Qiaochu Yuan timeline score: 11
Nov 28, 2020 at 4:45 history asked Alec Rhea CC BY-SA 4.0