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Every now and again I will have a very specific question about a paper or book, for which I think there is a high likelihood that only the author(s) of the paper or book can give a definite answer. However, I also often think it is the case that the answer to my question would be of general interest. I am thus torn between asking the author directly, or asking on mathoverflow (or math.stackexchange, depending on the question), so that the answer will be available to everyone. (Until now I have mostly asked the author directly.) Thus I would like to know:

Are there any general rules for when to contact an author directly as opposed to asking a question on mathoverflow?

Here is the most recent such question which prompted me to bring this up on meta.mathoverflow:

Example quesiton: In A charaterization of simplicial localization functors and a discussion of DK equivalences Barwick and Kan state that, while there is no preferred localization functor from relative categories to simplicial categories, there is a preferred relativization functor from simplicial categories to relative categories. It is not apparent to me in which sense the relativization functor is "preferred". No alternative to this construction ever seems to be discussed, nor is there any discussion about how this construction is in any way canonical or "forced" upon us. Thus I would like to ask:

In which sense is the relativization functor "preferred".

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    $\begingroup$ You can always ask an author directly, provided that the author is a living person and you have the contact data, and you are always welcome to ask on-topic questions on MO. Questions of the type you suggest could sometimes be taken as "too localized" for MO -- but apart from this, what kind of advice are you hoping for? $\endgroup$
    – Stefan Kohl Mod
    Commented Dec 6, 2016 at 16:46
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    $\begingroup$ My question is about how to resolve the following dilemma: Ask such a question, which I think would be of general interest, in a public forum, where the discussion of the question will be seen by everyone, but risk not getting an answer, as opposed to, asking the author in private, obtain an answer with high likelihood, but also increase the likelihood, that the answer will never be available to the public. $\endgroup$
    – Adrian Clough
    Commented Dec 7, 2016 at 9:11
  • $\begingroup$ To more specifically answer the question of @StefanKohl of what advise I was hoping for: I was hoping a) for ideas on how to properly weigh the two sides in the dilemma considered in my previous comment, and b) to be made aware of aspects of the problem I hadn't considered, such as such questions having an inherent propensity of possibly being too localized, or such nitpicking might touch upon issues that an author might not want to discuss in a public forum, as suggested in Gerhard's answer. $\endgroup$
    – Adrian Clough
    Commented Dec 7, 2016 at 9:17

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Upon thinking a little longer about my question, it seems to me that the following should often constitute a sensible procedure:

If you think the answer would be of public interest, ask on mathoverflow first. If you do not receive an answer, ask the author directly, point out that you have already asked the question on mathoverflow, and request permission, to post the author's answer on mathoverflow, in the case that the author decides to answer you directly.

This is based on the observations, that, firstly, it seems dangerous to make too strong assumptions about, what only the author(s) can answer, and secondly, that this way you will automatically have established the means by which the sought information is to be made public.

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Stefan Kohl has the right idea, which I amplify.

Authors are usually interested in sincere feedback and appropriate level questions about their work. It is not clear to me how your question will be received by the author, but usually the worst that happens is that you get no response. I thus recommend that you contact the author first, especially if issues arise that the author might prefer not to handle in a public forum.

Such issues notwithstanding, well intentioned comments, critiques, and questions of published work should be publicly available. Some of these are not suitable for the MathOverflow forum ( due to length or breadth or the fact that none of the members may be able to take a stab at an answer , or other reasons ), but the example you post seems suitable for MathOverflow to ( a non expert like) me.

Gerhard "More A Guideline Than Rule" Paseman, 2016.12.06.

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