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I do believe it is a trivial question. But unfortunately I don't know where I can find an answer.

Where could I find the answer to the following question?

If $S$ is a small category and $X$ is a quasi-topos, is $\operatorname{Fun} (S, X)$ a quasi-topos? If the answer is "no", what would be a nice counterexample? Would it be PsTop?

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Do you know the book 'Higher Topos Theory'? It might have an answer in there. –  Berci Jun 17 '14 at 20:26
@Berci Do you know what a quasitopos is? It's not a quasicategory! –  Zhen Lin Jun 17 '14 at 20:36

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