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In HTT, a version of the adjoint functor theorem for (locally) presentable infinity categories is proven (Corollary Is there a more refined version of this somewhere, which more closely resembles Freyd’s original version? I.e., is there a version for infinity categories which are not necessarily (locally) presentable, but requires a solution set condition? If so, a reference would be fantastic. Thanks!

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Perhaps one can work this out by oneself? After all, the adjoint functor has always a canonical representation as a colimit/limit, and the sole purpose of the solution set condition is to provide a small cofinal subcategory so that the colimit/limit exists. So then one has to look for the appropriate notions for $\infty$-categories. – Martin Brandenburg Jun 19 '12 at 9:18
I agree with you in principle Martin. However, I still haven't figured out how to prove this question (…) in the infinity context, and the classical way to prove the adjoint functor theorem uses this result for 1-categories. Any ideas? – David Carchedi Jun 19 '12 at 17:07

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