2023/10/30 by Keisuke Hoshino, Hoshino, Keisuke, Nasu, Hayato · 1 citation
Computer Science · #18A32 #18B10 #18E08 #18N10 #Category Theory (math.CT) #FOS: Mathematics #Multimodal Machine Learning Applications #Natural Language Processing Techniques #Speech and dialogue systems
paper · pdf · doi:10.48550/arxiv.2310.19428
openalex publication_date 2023/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.