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Categorical structures enriched in a quantaloid: tensored and cotensored categories

Isar Stubbe
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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.

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Isar Stubbe. 2004-11-16. Categorical structures enriched in a quantaloid: tensored and cotensored categories. https://arxiv.org/abs/math/0411366

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