Double categories of relations relative to factorisation systems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916578282438656 |
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| author | Hoshino, Keisuke Nasu, Hayato |
| author_facet | Hoshino, Keisuke Nasu, Hayato |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19428 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double categories of relations relative to factorisation systems Hoshino, Keisuke Nasu, Hayato Category Theory 18B10, 18E08, 18N10, 18A32 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. |
| title | Double categories of relations relative to factorisation systems |
| topic | Category Theory 18B10, 18E08, 18N10, 18A32 |
| url | https://arxiv.org/abs/2310.19428 |