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Does anything prevent a codensity monad construction for the inclusion of FinCat into Cat?
Mike’s asking about the inclusion of finitely presented $\infty$-groupoids, back here. Does changing ’finite’ to ’finitely presented’ make a difference to my question?
I guess there’s also the inclusion of finite sets into $Cat$ as discrete categories. That might be nearer ultracategories.
Added a reference
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