article · ArXiv.org · 2025

Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry

García, Javier Gutiérrez, Höhle, Ulrich

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Abstract

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.

Cite this paper

APA 7

García, J. G., & Höhle, U. (2025). Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry. ArXiv.org.

MLA 9

García, Javier Gutiérrez, and Ulrich Höhle. “Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry.” ArXiv.org, 2025.

Chicago

García, Javier Gutiérrez, and Ulrich Höhle. 2025. “Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry.” ArXiv.org.

Harvard

García, J.G. and Höhle, U. (2025) ‘Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry’, ArXiv.org.

BibTeX

@article{garcia2025quantaloid,
  title = {{Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry}},
  author = {García, Javier Gutiérrez and Höhle, Ulrich},
  journal = {ArXiv.org},
  year = {2025}
}

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