Timeline for On the definition of small categories in SGA4
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 6, 2023 at 2:17 | vote | accept | LOCOAS | ||
| Feb 5, 2023 at 10:33 | answer | added | Peter LeFanu Lumsdaine | timeline score: 6 | |
| Feb 5, 2023 at 9:42 | answer | added | LOCOAS | timeline score: 1 | |
| Jan 27, 2023 at 15:04 | comment | added | Zhen Lin | You are not wrong in the narrow sense but at the same time I think it is clear to you what the authors actually meant, so you are wrong to make a fuss of it. | |
| Jan 26, 2023 at 1:22 | comment | added | LOCOAS | @abx What you are saying is completely correct. We can interpret all claims in the proper sense. However, I am afraid that the above assertion about the smallness of the pair may produces errors in various places. So I would like to know if I am wrong in the above discussion. | |
| Jan 25, 2023 at 14:36 | comment | added | abx | In my view this is a completely artificial problem. We all know very well what is a small category, don't we? | |
| Jan 25, 2023 at 12:15 | comment | added | LOCOAS | @LSpice My source is exactly the part pointed out by abx. | |
| Jan 25, 2023 at 12:12 | comment | added | LOCOAS | @abx If that were the case, we would have to treat a category as an ordered pair of a set of morohisms, compositions, and so on. In that case, we end up with the same problem. | |
| Jan 25, 2023 at 12:08 | comment | added | LOCOAS | @Zhen Lin In page 2 of SGA 4 (see abx's link above), he says 'On dit qu’un ensemble est U-petit (ou, quand aucune confusion n’en résulte, petit) s’il est isomorphe à un élément de U.' | |
| Jan 25, 2023 at 10:39 | comment | added | Zhen Lin | It has been a long time since I looked at SGA 4 but do they actually define smallness as you say...? My impression was that they define a notion that is not bijection-invariant. | |
| Jan 25, 2023 at 5:06 | comment | added | abx | In the new edition of SGA 4, there is an editor's footnote on p. 2: "A category is viewed as a set of arrows". | |
| Jan 25, 2023 at 4:33 | comment | added | LSpice | Could you refer specifically to where this definition occurs? | |
| Jan 25, 2023 at 3:01 | history | asked | LOCOAS | CC BY-SA 4.0 |