Categorical structures enriched in a quantaloid: tensored and cotensored categories

Details Categorical structures enriched in a quantaloid: tensored and cotensored categories Categorical structures enriched in a quantaloid: tensored and cotensored categories

2004-11-16

arxiv.org/abs/math/0411366v1

Mathematics

Category Theory

19 pages

Scientific paper

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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