广义连续 Posets 的石头表示法

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-01-16 DOI:10.1007/s10485-023-09761-w

Ao Shen, Qingguo Li

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引用次数: 0

摘要

在本文中，我们介绍了广义连续实在的概念，并提出了它们的拓扑对偶性。此外，我们还证明了广义连续实在和连续态的范畴与 F 空间和 F 态的范畴是二重等价的。特别是，我们还得到了一些特例，如posets、域、连续网格和连接半网格的拓扑表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Stone Representations for Generalized Continuous Posets

In this paper, we introduce the concepts of generalized continuous posets and present topological dualities for them. Moreover, we show that the category of generalized continuous posets and continuous morphisms is dually equivalent to the category of F-spaces and F-morphisms. In particular, some special cases are obtained, such as the topological representations for posets, domains, continuous lattices and join-semilattices.

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

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.