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".