Timeline for compact elements and continuous functors
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2011 at 5:58 | comment | added | Ben Sprott | I also think that the n-categorical framework is at work here too. | |
| Apr 11, 2011 at 5:57 | 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 7:50 | comment | added | Ben Sprott | Thanks very much. I might be able to start working on this a bit more now. | |
| Apr 8, 2011 at 1:41 | comment | added | Todd Trimble | Hi Chris -- I was in the middle of writing my answer and didn't see your comment, which contains much of what I said. | |
| Apr 8, 2011 at 1:39 | answer | added | Todd Trimble | timeline score: 4 | |
| Apr 8, 2011 at 1:36 | answer | added | Finn Lawler | timeline score: 2 | |
| Apr 8, 2011 at 1:35 | comment | added | Chris Heunen | The equivalent of compact elements could be the following: an object $X$ is called finitely presentable when $\mathrm{Hom}(X,-)$ preserves directed colimits. The equivalent of a Scott domain would then be a locally finitely presentable category: one in which every object is a colimit of finitely presentable ones. The nLab page doesn't have many pointers, but Adamek and Rosicky have a nice book about the topic (albeit not oriented towards domains). | |
| Apr 8, 2011 at 0:41 | history | asked | Ben Sprott | CC BY-SA 3.0 |