Scholarlink

<p>The concept of pseudo ordered sets is a generalization of posets by removing the requirement of transitivity. The lack of transitivity in pseudo ordered sets prevents the direct application of standard completions for posets. This paper presents a unified framework for constructing completions of pseudo ordered sets. Our approach involves directly selecting families of subsets, which generalizes renowned standard completions for posets. We introduce suitable morphisms on pseudo ordered sets and characterize our completion construction by means of a universal property. This characterization establishes reflective relationships between categories of pseudo ordered sets and the category of complete trellises.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Standard Completions for Pseudo Ordered Sets

  • 期刊论文

  • 发表日期：

    2025年9月15日

查看全文
  • Zhongxi Zhang

摘要

The concept of pseudo ordered sets is a generalization of posets by removing the requirement of transitivity. The lack of transitivity in pseudo ordered sets prevents the direct application of standard completions for posets. This paper presents a unified framework for constructing completions of pseudo ordered sets. Our approach involves directly selecting families of subsets, which generalizes renowned standard completions for posets. We introduce suitable morphisms on pseudo ordered sets and characterize our completion construction by means of a universal property. This characterization establishes reflective relationships between categories of pseudo ordered sets and the category of complete trellises.