A Topological Duality for Monotone Expansions of Semilattices

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2022-08-29 DOI:10.1007/s10485-022-09690-0

Ismael Calomino, Paula Menchón, William J. Zuluaga Botero

引用次数: 0

Abstract

In this paper we provide a Stone style duality for monotone semilattices by using the topological duality developed in S. Celani, L.J. González (Appl Categ Struct 28:853–875, 2020) for semilattices together with a topological description of their canonical extension. As an application of this duality we obtain a characterization of the congruences of monotone semilattices by means of monotone lower-Vietoris-type topologies.

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半格单调展开的拓扑对偶性

本文利用S. Celani, L.J. González (Appl Categ Struct 28:853-875, 2020)提出的半格拓扑对偶性及其正则扩展的拓扑描述，给出了单调半格的Stone型对偶性。作为这一对偶性的应用，我们利用单调下维型拓扑得到了单调半格同余的一个表征。

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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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.