Categorical structures enriched in a quantaloid: projective cocomplete categories
نویسنده
چکیده
We study the different guises of the projective objects in Cocont(Q): they are the “completely distributive” cocomplete Q-categories (the left adjoint to the Yoneda embedding admits a further left adjoint); equivalently, they are the “totally continuous” cocomplete Q-categories (every object is the supremum of the presheaf of objects “totally below” it); and also are they the Q-categories of regular presheaves on a regular Q-semicategory. As a particular case, the Q-categories of presheaves on a Q-category are precisely the “totally algebraic” cocompleteQ-categories (every object is the supremum of the “totally compact” objects below it). We think that these results should be part of a yet-to-beunderstood “quantaloid-enriched domain theory”.
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