The fact that equalizers in the context of strongly Hausdorff locales (similarly like those in classical spaces) are closed is a special case of a standard categorical fact connecting diagonals with general equalizers. In this paper we analyze this and related phenomena in the category of locales. Here the mechanism of pullbacks connecting equalizers is based on natural preimages that preserve a number of properties (closedness, openness, fittedness, complementedness, etc.). Also, we have a new simple and transparent formula for equalizers in this category providing very easy proofs for some facts (including the general behavior of diagonals). In particular we discuss some aspects of the closed case (strong Hausdorff property), and the open and clopen one.

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关于语言环境类别中的均衡器

强 Hausdorff 区域环境中的均衡器（类似于经典空间中的均衡器）是封闭的这一事实是连接对角线与一般均衡器的标准分类事实的特例。在本文中，我们分析了语言环境类别中的这一现象和相关现象。在这里，连接均衡器的回调机制基于保留许多属性（封闭性、开放性、适合性、互补性等）的自然原像。此外，我们为此类中的均衡器提供了一个新的简单透明的公式，为某些事实（包括对角线的一般行为）提供了非常简单的证明。我们特别讨论了封闭案例（强 Hausdorff 性质）以及开放和开放案例的某些方面。