Timeline for Functor category's objects fail to be a class?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2013 at 7:14 | comment | added | Fred Rohrer | Although it does not solve the problem under discussion, the reference for the general description of Bourbaki's technique mentioned by Mariano is E.II.6.9. | |
| Oct 30, 2013 at 4:25 | answer | added | Theo Johnson-Freyd | timeline score: 5 | |
| Oct 28, 2013 at 16:18 | comment | added | Philippe Gaucher | Yes there is a trick: for every universe $\mathcal{U}$, postulate the existence of a successor universe $\mathcal{U}^+$ : this is used for example in "Homotopy Limit Functors on Model Categories and Homotopical Categories" by Dwyer, Hirschhorn, Kan, Smith. | |
| Oct 27, 2013 at 19:32 | comment | added | Zhen Lin | The fact that equivalence classes are too big is just a technical inconvenience and can be sidestepped using Scott's trick in ZF set theory. In the particular case of $K$-theory you can cheat even more and just restrict your attention to the modules whose underlying set is a subset of a fixed set. On the other hand the fact that there are too many functors between general categories is not something that can be fixed with a trick. | |
| Oct 27, 2013 at 19:05 | comment | added | Mariano Suárez-Álvarez | Bourbaki, for example, deals with this sort of issue by showing that the equivalence relations used are "totalizing" (or some other similar word) You can see an example of this in the section where he constructs the Brauer group. | |
| Oct 27, 2013 at 18:49 | answer | added | Yuri Sulyma | timeline score: 6 | |
| Oct 27, 2013 at 18:33 | history | asked | user27976 | CC BY-SA 3.0 |