Double categories of relations relative to factorisation systems

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 verti...

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Bibliographic Details
Main Authors Hoshino, Keisuke, Nasu, Hayato
Format Journal Article
LanguageEnglish
Published 30.10.2023
Subjects
Mathematics - Category Theory
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Summary: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.
DOI:10.48550/arxiv.2310.19428