We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on a category $\mathcal{C}$. Not only this result allows to obtain a categorical counterpart $\mathbb{P}$ of the Császár-Pervin quasi-uniformity $\mathcal{P}$, that we characterize as a transitive quasi-uniformity compatible with an idempotent interior operator, but also permits to describe those topogenous orders that are induced by a transitive quasi-uniformity on $\mathcal{C}$. The categorical counterpart ${\mathbb{P}}^{⁎}$ of ${\mathcal{P}}^{-1}$ is characterized as a transitive quasi-uniformity compatible with an idempotent closure operator. When applied to other categories outside topology $\mathcal{P}$ allows, among other things, to generate a family of idempotent closure operators on Grp, the category of groups and group homomorphisms, determined by the normal closure.

我们证明了幂等封闭运算符与类别上所谓的饱和拟均匀结构之间的一一对应关系 $\mathcal{C}$。不仅这个结果允许获得绝对的对应物$\mathbb{P}$ Császár-Pervin准均匀性 $\mathcal{P}$，我们将其表征为与幂等内部算子兼容的传递拟一致，但也允许描述由传递拟拟一致导致的那些拓扑阶 $\mathcal{C}$。绝对对应${\mathbb{P}}^{⁎}$ 的 ${\mathcal{P}}^{-\mathrm{1个}}$表征为与幂等闭合算符兼容的传递准均匀性。当应用于拓扑之外的其他类别时$\mathcal{P}$除了其他功能外，它还可以在Grp上生成一族幂等闭合运算符，该群是正常闭合确定的组和组同态的类别。