Double Categories of Relations Relative to Factorisation Systems

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2025-03-06 DOI:10.1007/s10485-025-09799-y

Keisuke Hoshino, Hayato Nasu

引用次数: 0

Abstract

We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension scheme, and the second focuses on a specific class of vertical arrows defined solely double-categorically. We organise diverse classes of double categories of relations and correlate them with significant classes of factorisation systems. Our framework embraces double categories of spans and double categories of relations on regular categories, which we meticulously compare to existing work on the characterisations of bicategories and double categories of spans and relations.

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与因式分解系统有关的双重关系类别

我们将双范畴关系相对于稳定的正交分解系统。此外，我们用两种方法给出了关系的相对双重范畴的特征。第一个使用了一个一般化的理解方案，第二个关注的是一组特定的垂直箭头，它们完全是双范畴定义的。我们组织了关系双范畴的不同类，并将它们与分解系统的重要类联系起来。我们的框架包含了常规范畴上的双范畴的跨度和关系的双范畴，我们仔细地将其与现有的双范畴和双范畴的跨度和关系的特征进行了比较。

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.