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I'm slowly going through some topos theory papers by Lawvere. In almost every paper, there are many small sayings and sometimes entire sentences which I do not understand and have never explicitly seen in books. I feel like understanding these is essential to gain insight into the workings of toposes.

A typical example (from the paper Quantifiers and sheaves) is the axiom of choice as 0-dimensionality geometrically.

Should I ask about several such pharses in a single question or actually write up a separate one each time?

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    $\begingroup$ Let me add to quid's answer that it is crucial to make your question self-contained. In particular it is not reasonable to expect that in order to understand your question, people read the paper you ask about. $\endgroup$
    – Stefan Kohl Mod
    Commented Dec 25, 2015 at 22:40

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As a rule, it is better to ask one thing per question, as opposed to asking multiple vaguely related things in one questions-post. (For one thing, what will you do if only half of the things you ask get answered in the answers you receive?)

In your case it depends a bit how closely related the things are. If some of them are very closely related and each seems short it can still make sense to ask them in one. The test is really do you ask one question relating to several quotes or do you ask multiple questions. Try to do the former.

But when in doubt better keep it narrow, and put some effort into asking this one thing well. Then, wait and see how it goes, before you ask other related questions.

In brief:

  • Do not ask a laundry-list style question.

  • Do not ask a bunch of similarly themed questions at the same time.

  • Do ask one well-crafted question, and base further decisions on the feedback you get.

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    $\begingroup$ It should be added that well-crafted questions undergo more than one revision, and that the community hopes but does not expect that you get it right on the first try. We do expect that you will respond to feedback in a way for mutual benefit to you and to the community. Gerhard "When In Doubt, Read FAQ" Paseman, 2015.12.25 $\endgroup$
    – Gerhard Paseman
    Commented Dec 25, 2015 at 19:44

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