Hey again everybody,

So last night I was trying to prove that if we take the (∞,1)-category of (∞,1)-categories use the left adjoint to the inclusion of the n-truncated objects, we get a localization at a reasonable subcategory of things that we could call a quasicategory of (n,1)-categories or n-categories. I’m aware that all I can really hope to get is a category of objects which are equivalent to honest n-categories. Is this a reasonable thing to try to do? It seems like it would make proving things about n-categories, for instance, a monadicity theorem, easier. Perhaps this is well known, and I just haven’t searched well enough. Do you guys know?

-Jon

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