标题： 通过关系提升的广义幂局部对象 显示英文标题

标题： Generalized powerlocales via relation lifting

摘要： 本文介绍了框架范畴上的一个自函子$\VT$，该自函子由满足某些约束条件的范畴$\Set$上的自函子$\T$参数化。 这在某种意义上推广了Johnstone的Vietoris幂局部体构造，因为他的构造是通过将$\T$取为有限协变幂集函子得到的。 我们从框架$\bbL$构造$\T$-幂局部体$\VT \bbL$的方法基于对偶代数逻辑的思想，并明确阐明了Vietoris构造与Moss的对偶代数覆盖模态之间的联系。 我们展示如何将集合函子之间的某些自然变换扩展为$\T$-幂局部域函子之间的自然变换。 最后，我们证明运算$\VT$保持框架的一些性质，例如正则性、零维性和零维性与紧性的结合。 显示英文摘要

摘要： This paper introduces an endofunctor $\VT$ on the category of frames, parametrized by an endofunctor $\T$ on the category $\Set$ that satisfies certain constraints. This generalizes Johnstone's construction of the Vietoris powerlocale, in the sense that his construction is obtained by taking for $\T$ the finite covariant power set functor. Our construction of the $\T$-powerlocale $\VT \bbL$ out of a frame $\bbL$ is based on ideas from coalgebraic logic and makes explicit the connection between the Vietoris construction and Moss's coalgebraic cover modality. We show how to extend certain natural transformations between set functors to natural transformations between $\T$-powerlocale functors. Finally, we prove that the operation $\VT$ preserves some properties of frames, such as regularity, zero-dimensionality, and the combination of zero-dimensionality and compactness.