Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories

2004/09/24 by Isar Stubbe, Stubbe, Isar · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rough Sets and Fuzzy Logic #math.CT

paper · pdf · doi:10.48550/arxiv.math/0409475

21 pages

arxiv created 2004/09/24 · openalex publication_date 2004/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study presheaves on semicategories enriched in a quantaloid: this gives rise to the notion of regular presheaf. A semicategory is regular when its representable presheaves are regular, and its regular presheaves then constitute an essential (co)localization of the category of all of its presheaves. The notion of regular semidistributor allows to establish the Morita equivalence of regular semicategories. Continuous orders and Omega-sets provide examples.

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