Quantale Valued Sets: Categorical Constructions and Properties

IF 0.6 3区数学 Q2 LOGIC

Studia Logica Pub Date : 2024-09-18 DOI:10.1007/s11225-024-10138-w

José G. Alvim, Hugo L. Mariano, Caio de A. Mendes

引用次数: 0

Abstract

This work mainly concerns the—here introduced—category of \(\mathscr {Q}\)-sets and functional morphisms, where \(\mathscr {Q}\) is a commutative semicartesian quantale. We prove it enjoys all limits and colimits, that it has a classifier for regular subobjects (a sort of truth-values object), which we characterize and give explicitly. Moreover: we prove it to be \(\kappa \)-locally presentable, (where \(\kappa =max\{|\mathscr {Q}|^+, \aleph _0\}\)); we also describe a hierarchy of monoidal structures in this category.

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量值集：分类构造和属性

这项工作主要涉及这里引入的（\(\mathscr {Q}\）集合和函数态的类别，其中（\(\mathscr {Q}\）是一个交换半笛卡尔量子。我们证明它享有所有的极限和 colimits，它有一个规则子对象（一种真值对象）的分类器，我们对它进行了描述并给出了明确的定义。此外：我们证明它是\(\kappa \)-locally presentable的（其中\(\kappa =max\{|\mathscr {Q}|^+, \aleph _0\}\））；我们还描述了这个范畴中的单元结构的层次。

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

Studia Logica MATHEMATICS-LOGIC

CiteScore

1.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The leading idea of Lvov-Warsaw School of Logic, Philosophy and Mathematics was to investigate philosophical problems by means of rigorous methods of mathematics. Evidence of the great success the School experienced is the fact that it has become generally recognized as Polish Style Logic. Today Polish Style Logic is no longer exclusively a Polish speciality. It is represented by numerous logicians, mathematicians and philosophers from research centers all over the world.