G. Bezhanishvili, F. Dashiell Jr., A. Razafindrakoto, J. Walters-Wayland
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引用次数: 0
Abstract
We develop a hierarchy of semilattice bases (S-bases) for frames. For a given (unbounded) meet-semilattice A, we analyze the interval in the coframe of sublocales of the frame of downsets of A formed by all frames with the S-base A. We study various degrees of completeness of A, which generalize the concepts of extremally disconnected and basically disconnected frames. We introduce the concepts of D-bases and L-bases, as well as their bounded counterparts, and show how our results specialize and sharpen in these cases. Classic examples that are covered by our approach include zero-dimensional, completely regular, and coherent frames, allowing us to provide a new perspective on these well-studied classes of frames, as well as their spatial counterparts.
我们建立了一个框架的半格基（S-base）层次结构。对于给定的（无界的）相遇半网格 A，我们分析了由具有 S 基 A 的所有网格形成的 A 的下集网格的子网格的共帧区间。我们研究了 A 的各种完备度，它们概括了极端断开和基本断开网格的概念。我们引入了 D 基和 L 基及其有界对应物的概念，并展示了我们的结果在这些情况下是如何特殊化和锐化的。我们的方法涵盖的经典例子包括零维框架、完全规则框架和相干框架，使我们能够以全新的视角看待这些研究得很透彻的框架类别及其空间对应物。
期刊介绍：
Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant.
Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.
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