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Morgan Rogers (he/him) (Jun 12 2021 at 10:14):Based on Scott Garrabant's recent talk on finite factored sets, transcribed by him here, @Gurkenglas started a category theory discussion on the MIRI (AI alignment) Discord server on a possible approach to a categorical construction of a category of factored sets, and more generally of factored posets or categories, with the finiteness condition removed. Since I was the only person engaging there (and since I have limited time) I invited them here to get more input.
Morgan Rogers (he/him) (Jun 12 2021 at 10:14):@Gurkenglas feel free to reproduce the basics of your construction here :grinning_face_with_smiling_eyes: