Let $L$ be a regular language.
Is the language $L_2 = \{ ww | w \in L \}$ context-free? Does it have a name?
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Not regular, not even when $L={a,b}^*$. See for example https://cs.stackexchange.com/q/11759, https://cs.stackexchange.com/q/38459/4287 or https://cs.stackexchange.com/q/45681/4287 . – Hendrik Jan Oct 27 '23 at 11:53
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@HendrikJan thanks, see my edit, I'm also interested in the name of the language – user1868607 Oct 27 '23 at 11:55
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OK, I should have added the language for $L={a,b}^*$ is not context-free. Usually one of the standard examples for which the pumping lemma for context-free languages is applied. I do not know of a well-established name. The last question I linked to uses "repeat(L)". – Hendrik Jan Oct 27 '23 at 13:06