论文标题
完成K类别的简单估值
Completing Simple Valuations in K-categories
论文作者
论文摘要
我们证明，简单估值的单调与Keimel和Lawson的K-Completion KC在每个K类别上定义了一个单元KC O VS。我们还将KC O VS的Eilenberg-Moore代数描述为弱的本地convex k-cones，以及其代数的Morphisms，及其代数的Mephisms及其持续的linear linear linear mimaps。此外，我们明确描述了KC上VS的分布定律，这使我们能够证明任何局部凸的k完成（分别是局部局部凸，局部线性）拓扑锥是局部凸（分别是局部局部局部，局部局部凸出，局部凸出，在局部呈线性线性）K-cone。我们还举了一个示例 - 带有顶部的cantor树 - 显示简单估值的DCPO完成，这通常不是简单估值的d -completion，其中D是单调收敛空间和连续地图的类别。
We prove that Keimel and Lawson's K-completion Kc of the simple valuation monad Vs defines a monad Kc o Vs on each K-category A. We also characterize the Eilenberg-Moore algebras of Kc o Vs as the weakly locally convex K-cones, and its algebra morphisms as the continuous linear maps. In addition, we explicitly describe the distributive law of Vs over Kc, which allows us to show that the K-completion of any locally convex (respectively, weakly locally convex, locally linear) topological cone is a locally convex (respectively, weakly locally convex, locally linear) K-cone. We also give an example - the Cantor tree with a top - that shows the dcpo-completion of the simple valuations is not the D-completion of the simple valuations in general, where D is the category of monotone convergence spaces and continuous maps.
