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Elisha Goldman (Oct 03 2025 at 19:38):Rel is equivalently:
The first definition comes from the regular category structure on Set and the second comes from its properties as a topos; has the second definition been generalized to arbitrary topoi yet, and if it has, when are the two equivalent?
Mike Shulman (Oct 03 2025 at 19:51):Yes, and always, essentially from the universal property of power objects in a topos.
Elisha Goldman (Oct 03 2025 at 19:55):Ah, well it's good to have a simple answer lol. Do they all have similar characterizations of the EM category too?
Notification Bot (Oct 03 2025 at 19:55):Elisha Goldman has marked this topic as resolved.
Mike Shulman (Oct 03 2025 at 23:47):The EM-category of the power-object monad on any topos is the category of internal suplattices in that topos.
John Baez (Oct 04 2025 at 13:31):A question in category theory is never resolved, it just keeps getting more interesting the more you dig into it. :wink: