Timeline for Why do we need filtered categories to index ind-objects?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2015 at 19:01 | comment | added | Dylan Wilson | French, but math french isn't difficult | |
| Jul 10, 2015 at 17:54 | comment | added | David White | @DylanWilson Do you read it in French or has someone translated it to English? | |
| Jul 10, 2015 at 6:32 | comment | added | Eric Wofsey | Note that ordinal-indexed diagrams (as opposed to directed set-indexed diagrams) are not sufficient to get all ind-objects. However, all filtered colimits can be computed as iterated ordinal-indexed colimits (assuming the latter exist). The point is that if you have something like the poset of finite subsets of an uncountable set, you can only turn it into an ordinal-indexed colimit if you are able to take intermediate colimits along the way (corresponding to initial segments of some well-ordering of your uncountable set). | |
| Jul 10, 2015 at 5:48 | comment | added | category_student | Thanks a lot. That's exactly what I was looking for. Perhaps this is folklore, but as an outsider trying to learn - it is quite strange that is not discussed in more references on the topic, which leave you just with the definition of filtered category and a sense of puzzlement. | |
| S Jul 10, 2015 at 5:44 | history | answered | Dylan Wilson | CC BY-SA 3.0 | |
| S Jul 10, 2015 at 5:44 | history | made wiki | Post Made Community Wiki by Dylan Wilson |