In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and gives many more. The theorem depends on a formal approach to exactness properties proposed in this paper, which is based on the theory of sketches. Our stability theorem has applications in proving theorems that establish links between exactness properties, as well as in establishing embedding (representation) theorems for categories defined by exactness properties.

中文翻译：

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论亲完成下精确性性质的稳定性

在本文中，我们制定并证明了pro-completion下精确性稳定性的一般定理，它统一了文献中的几个这样的定理并给出了更多。该定理依赖于本文提出的精确性属性的形式化方法，该方法基于草图理论。我们的稳定性定理可用于证明在精确性属性之间建立联系的定理，以及为由精确性属性定义的类别建立嵌入（表示）定理。