My understanding is that MSE is supposed to be a repository of high quality questions and answers about mathematics. What constitutes a high quality question is of course (to some extent) a matter of personal opinion, but according to mine, a question which meets most of the following criteria is definitely "high quality enough" and doesn't deserve to be closed :
- It is clear and understandable by most people who are familiar with the topic in the broad sense (i.e. the tags of the question). For instance the question cited by the OP is perfectly clear to anyone who has studied/is studying category theory, but it's totally impenetrable to me as I know nothing about this topic. That latter point should never be a reason to close a question.
- It is well motivated by examples or some explanation of how the question came about (questions asking about terminology don't necessarily need to satisfy this by the way). For instance the question Quantile function is the almost surely left inverse of CDF I answered a while ago arose naturally as the OP was reading a Wikipédia article about the quantile function. I believe that amount of context is sufficient in general.
- It is useful and/or helpful in the sense that either many students of that topic are likely to encounter a similar question at some point, or people generally interested in that topic are likely to gain valuable insights by answering this question and/or answering it themselves. Of course, this point is rather subjective and best evaluated by people who are familiar enough with the topic. I think that How discontinuous can a derivative be? is a good example of such a question, which is relatively short and full of technical terms which are not defined. I suspect some people would have voted to close it if it was posted today by a low-rep user, however it (and its answer !) is one of the most valuable real analysis questions on this site
- It is an original question which hasn't been asked/answered before on this site. Not much explanation needed on this last point, but as an illustration consider the question $L^p$ and $L^q$ space inclusion : if it was asked for the first time today, I expect that it would be closed within 24 hours, however this is again an extremely valuable question for this site that should stay open and have an answer that we can reference to in the future.
As a rule of thumb, if 3 out of 4 of the above criteria are met, the question should not be closed. If you see an "edge case" and you're not sure whether you should vote to close or leave open, just skip that question and do not vote to close it. As a converse of the above list, I would say that any of the below reasons alone should never be ground for closing a question :
- The question is not understandable/interesting for people who are not familiar with the topic.
- The question doesn't include OP's attempt/thoughts on solving it.
- The question is too short (some one sentence questions are extremely helpful and valuable).
Of course, this is only my personal opinion, and juding by the conversation so far, it seems like we won't reach a community-wide consensus. My suggestion would thus be, for people who see an interesting question they are afraid will get closed, to try and "protect" the question with a comment along those lines
to potential close voters : this may appear as a Problem Statement Question for those unfamiliar with [topic XXX], but it is in fact a valuable question because [reasons YYY] which, as far as I can tell, has not been asked here before. As others interested in [topic XXX] will most likely find this question useful, please do not vote to close it.
Of course editing the question to add more context, as Sarvesh Ravichandran Iyer did e.g. for this question, is definitely the most effective way to have it remain open, but in my opinion it shouldn't be necessary.