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We know that a combinatorial model category has a small presentation.

Is an enriched version of this theorem known? The closest I could find is: Guillou, May - Enriched model categories and presheaf categories (2011), but (as far as I understand) it discusses a narrower question (sufficient conditions for an enriched model category to be Quillen equivalent to a presheaf category with the projective model structure).

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    $\begingroup$ This is supposed to be in HTT Appendix A.3, but looking at it now I think you'll have to piece it together from the diagram category part + the localization part. $\endgroup$
    – Tim Campion
    Commented May 23, 2023 at 2:52
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    $\begingroup$ See also the more general Conjecture 1.10 in the paper arxiv.org/abs/2110.04679v2; as far as I know, it has not been resolved. $\endgroup$
    – Dmitri Pavlov
    Commented May 23, 2023 at 5:02
  • $\begingroup$ @ArshakAivazian Could you please state precisely what you mean by "an enriched version of this theorem"? Depending on what would satisfy you, I might be able to write an answer. $\endgroup$
    – David White
    Commented Dec 17, 2023 at 14:37

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