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