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Hi, Suppose we define a dcpo of categories, where the ordering relation is a suitably restricted functor. The functor is restricted specificallly so that our collection and ordering reltion form a dcpo. In this dcpo of categories, the familiar categories, those we find in most any textbook, are the compact elements of this dcpo? I feel I also need to add that the dcpo we want is the largest dcpo of categories so defined. I've heard that terminology before.

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 This question is ill posed, not to mention that it provides no background. Do you think you defined a functor in your question (you did not), or do you want us to do it? And why? What good will come from making a dcpo whose elements are categories? – Andrej Bauer Nov 17 at 1:57
Actually, you sound like a troll to me. – Andrej Bauer Nov 17 at 1:58
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 Hi Ben, I highly recommend that you read some more MO questions and look over mathoverflow.net/howtoask and then revise this question. It would be much improved if you were to write a bit more: give some motivation, explain terms better, copyedit your text, .... Not only would it be easier for others of us to understand and answer your question, but writing your question clearly will help you to clarify your own thoughts. – Theo Johnson-Freyd Nov 17 at 4:27

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