Timeline for How should one call and use categories that are not locally small?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 2 at 20:09 | comment | added | Martin Brandenburg | Also there is of course the hom functor also for general categories, just take the large sets as the codomain. | |
| Dec 2 at 20:08 | comment | added | Martin Brandenburg | The claim that Fun(C,Set) is locally small when C is essentially small is wrong. See my answer at math.stackexchange.com/questions/3654695/… | |
| Oct 29, 2016 at 13:40 | comment | added | user337830 | Yes, that would be correct. | |
| Oct 29, 2016 at 13:33 | comment | added | Mikhail Bondarko | I was rather wondering whether it is fine to say that a very large category is locally small (if the Hom-sets are small). | |
| Oct 29, 2016 at 11:14 | comment | added | user337830 | You are welcome! Very large categories can be locally small. For instance, take a poset whose set of objects is a conglomerate (not even a class). However, I have to say that, 'naturally' arising very large categories are usually big. | |
| Oct 29, 2016 at 10:58 | comment | added | Mikhail Bondarko | Actually, this looks quite like a nice answer to the question (and may even be the best possible one for my purposes).:) You are most probably right in saying that "big categorical" issues depend on the choice of foundations; yet I wouldn't like to write much about this since I do not rely much on big categories. Note however that in his book "Triangulated categories" Neeman considers injective cogenerators of functor categories. I am doing nothing like this in my paper; yet I wonder which foundations are needed to justify arguments of this sort. | |
| Oct 29, 2016 at 10:52 | comment | added | Mikhail Bondarko | Thank you very much! So, is it fine to say that a very large category is locally small? | |
| Oct 29, 2016 at 10:25 | history | answered | user337830 | CC BY-SA 3.0 |