Presenting Quotient Locales

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2023-07-21 DOI:10.1007/s10485-023-09736-x

Graham Manuell

引用次数: 1

Abstract

It is often useful to be able to deal with locales in terms of presentations of their underlying frames, or equivalently, the geometric theories which they classify. Given a presentation for a locale, presentations for its sublocales can be obtained by simply appending additional relations, but the case of quotient locales is more subtle. We provide simple procedures for obtaining presentations of open quotients, proper quotients or general triquotients from presentations of the parent locale. The results are proved with the help of the suplattice, preframe and dcpo coverage theorems and applied to obtain presentations of the circle from ones for \(\mathbb {R}\) and [0, 1].

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表示商区域

能够根据其底层框架的表示来处理区域，或者等价地，根据它们分类的几何理论来处理区域，通常是很有用的。给定一个语言环境的表示，可以通过简单地附加附加关系来获得其子语言环境的表示，但是商数语言环境的情况更加微妙。我们提供了简单的程序来从父语言环境的表示中获得开商、适当商或一般三商的表示。利用拟合定理、预帧定理和dcpo覆盖定理对结果进行了证明，并应用于\(\mathbb {R}\)和[0,1]的圆表示。

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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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.