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Q-modules are Q-suplattices
Isar Stubbe
It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctri…
Categorical structures enriched in a quantaloid: tensored and cotensored categories
Isar Stubbe
Our subject is that of categories, functors and distributors enriched in a base quantaloid Q. We show how cocomplete Q-categories are precisely those which are tensored and conical…
Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories
Isar Stubbe
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 r…
Categorical structures enriched in a quantaloid: categories, distributors and functors
Isar Stubbe
We thoroughly treat several familiar and less familiar definitions and results concerning categories, functors and distributors enriched in a base quantaloid Q. In analogy with V-c…