Categorical structures enriched in a quantaloid: tensored and cotensored categories

Abstract

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 conically cocomplete, or alternatively, those which are tensored, cotensored and order-cocomplete. Bearing this in mind, we analyze how Sup-valued homomorphisms on Q are related to Q-categories. With an appendix on action, representation and variation.

19 pages

References in corpus (2)

• Categorical structures enriched in a quantaloid: categories, distributors and functors
• Categorical structures enriched in a quantaloid: regular presheaves, regular semicategories

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