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I am used to posting on MathOverflow problems with questions. However, now I am looking for the name of a mathematical object that I think already exists (and I would be happy to find reference recommendations about it).

Is MathOverflow appropriate for such questions, although I am not asking to discuss any (research) problem/solution?

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    $\begingroup$ You could have a look on the main site among the questions tagged (terminology) - to see whether some of them are similar to your question - and how they were received. $\endgroup$
    – Martin Sleziak
    Commented Dec 7, 2022 at 13:54

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Yes, such questions can certainly be on topic, providing they meet the usual criteria for good questions.

Theoretical answer: The general primary criterion is that a question should be about research-level mathematics — and asking for previous literature one some mathematical object is certainly about research-level mathematics (provided the object isn’t something extremely well-known, trivial, etc.) See also the reasoning in the answers/comments of Should this site be "a shortcut to substitute for literature searches"? — most of that applies here too, in particular about how to draw the line of what makes something “research-level”.

Practical answer: I’ve had several such questions positively-received.

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