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Apr 11, 2011 at 5:56 comment added Ben Sprott Hey, It looks like I am interested in yet a higher level of abstraction. When I asked about finitely present categories, I was being specific. I mean that categories themselves could be the elements of the domain. I apologize for the roughness with which I am speaking. I think the intuition I am working on is borrowed from the fact that the set of endomaps of a domain is also a domain. This is, itself, a path of abstraction. If the categories are the elements of the domain, then the compact objects which Todd talks aobut can be abstracted up into compact categories.
Apr 8, 2011 at 6:27 comment added Mike Shulman Functors that preserve filtered colimits are often called "finitary".
Apr 8, 2011 at 1:36 history answered Finn Lawler CC BY-SA 3.0