Abstract This paper presents a necessary and sufficient condition on a category C with weak finite limits for its exact completion C ex to be (locally) cartesian closed. A paper by Carboni and Rosolini already claimed such a characterisation using a different property on C , but we shall show that weak finite limits are not enough for their proof to go through. We shall also indicate how to strengthen the hypothesis for that proof to work. It will become clear that, in the case of ex/lex completions, their characterisation is still valid and it coincides with the one presented here.

中文翻译：

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关于精确完成的局部笛卡尔闭合

摘要 本文提出了具有弱有限极限的类别C 的充分必要条件，使其精确完成C ex 为（局部）笛卡尔封闭。Carboni 和 Rosolini 的一篇论文已经声称使用 C 上的不同属性进行了这种表征，但我们将表明弱有限限制不足以通过他们的证明。我们还将指出如何加强假设以使该证明有效。很明显，在 ex/lex 补全的情况下，它们的特征仍然有效，并且与此处介绍的特征一致。