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James Deikun (Apr 20 2025 at 19:31):Does taking the category of pseudo algebras of a 2-monad whose underlying 1-monad is accessible in a 2-category whose underlying 1-category is locally presentable result in another 2-category whose underlying 1-category is locally presentable?
Nathanael Arkor (Apr 20 2025 at 19:51):Assuming you care about the pseudo morphisms, then no, but such 2-categories do tend to be accessible. The reference for this kind of situation is Bourke's Accessible aspects of 2-category theory.
James Deikun (Apr 20 2025 at 20:25):Well, it's too bad there probably isn't a combinatorial model structure on clans, but it kind of makes sense there wouldn't be a good -category of them I guess.
James Deikun (Apr 20 2025 at 20:26):Wait, no, that doesn't make sense actually. But maybe that one's not presentable either.