Timeline for are quotients by equivalence relations "better" than surjections?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 9, 2018 at 22:47 | comment | added | Mike Shulman | @DavidRoberts Good point, I was too glib about that. I guess the dual notion of "system of quotients" would have to omit the composability if you want to include the usual notion of quotient set in ${\rm Set}$. However, it occurs to me that "quotients" of setOIDS do compose, so at least ${\rm Set}$ is equivalent to some category that has a system of quotients with composition. | |
| Dec 9, 2018 at 22:18 | comment | added | Kevin Buzzard | So "M-category" does not answer the question for surjections? | |
| Dec 9, 2018 at 19:52 | comment | added | David Roberts♦ | However, the standard construction of quotients doesn't naively form an M-category, as the 'set of equivalence classes with a map to it' isn't transitive: one gets sets of sets of equivalence classes. Perhaps there is a way to fix this, but I didn't see it with a (small amount of) thinking. | |
| Dec 9, 2018 at 9:08 | comment | added | Andrej Bauer | Thanks for the reference, I was aware of but failed to mention it. | |
| Dec 8, 2018 at 19:19 | history | answered | Mike Shulman | CC BY-SA 4.0 |