Timeline for What is the correct definition of localisation of a category?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2021 at 23:38 | vote | accept | Luke | ||
| Oct 7, 2018 at 10:24 | vote | accept | Luke | ||
| Jan 31, 2021 at 23:38 | |||||
| Oct 6, 2018 at 10:14 | comment | added | Denis Nardin | @LennartMeier Oops, wrong example. I still believe the overall point to be valid but let me retract it before I further embarass myself... | |
| Oct 6, 2018 at 10:09 | comment | added | Lennart Meier | @DenisNardin Maybe I'm slow, but it seems to me that the categories of abelian groups you describe are actually isomorphic because of the uniqueness of $0$ and $-$. | |
| Oct 5, 2018 at 23:31 | comment | added | Mike Shulman | @DenisNardin In mathematical practice, I agree with you (at least for "large" categories -- not in the technical sense). But there are places inside category theory (e.g. 2-categorical coherence theory) where using isomorphisms of categories (carefully, of course) can make certain things much easier, and so it can be useful to also be able to characterize categories by strict universal properties. But if you do it, you have to do it consistently. | |
| Oct 5, 2018 at 19:37 | comment | added | Denis Nardin | Honestly I would say that the only definition I'd consider "well-posed" is the one you call "weak localization". Relying on isomorphisms of categories is always a bit icky. | |
| Oct 5, 2018 at 18:38 | history | answered | Mike Shulman | CC BY-SA 4.0 |