Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912642642214912 |
|---|---|
| author | García, Javier Gutiérrez Höhle, Ulrich |
| author_facet | García, Javier Gutiérrez Höhle, Ulrich |
| contents | This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories and whose morphisms are left adjoint distributors admits an (epi, extremal mono)--factorization system. Furthermore, we prove that the category of cocomplete quantaloid-enriched categories satisfies the weak subobject classifier axiom, under stability conditions on the underlying quantaloid. As an application, we discuss how these structural results extend to quantale-valued sets, thereby generalizing the classical theory of $Ω$-valued sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry García, Javier Gutiérrez Höhle, Ulrich Category Theory This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories and whose morphisms are left adjoint distributors admits an (epi, extremal mono)--factorization system. Furthermore, we prove that the category of cocomplete quantaloid-enriched categories satisfies the weak subobject classifier axiom, under stability conditions on the underlying quantaloid. As an application, we discuss how these structural results extend to quantale-valued sets, thereby generalizing the classical theory of $Ω$-valued sets. |
| title | Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry |
| topic | Category Theory |
| url | https://arxiv.org/abs/2510.10162 |