Timeline for functors reflecting "isomorphism relations"?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 21, 2020 at 14:55 | comment | added | Pavel Čoupek | However, it seems to be the case that either way, "creating isomorphisms" should also include reflecting them, so there is (should be) some difference between this notion and "injectivity on isom. classes." | |
| Feb 21, 2020 at 14:50 | comment | added | Pavel Čoupek | @MartinBrandenburg I guess it depends on the definition of creating limits, there seems to be some debate around that as well: mathoverflow.net/questions/103065/… If you use Def. 1 in the above link, then I agree with what you are saying. If you use Def. 2, then it fits better this version (then the statement in both cases is "if it exists in the target, then it exists in the domain, and $F$ preserves it"). | |
| Feb 21, 2020 at 8:08 | comment | added | Martin Brandenburg | I am not sure if this analogy fits well. $F$ creates isomorphisms should mean that if $F(f)$ is inverse to $g$, then there is a unique morphism $f'$ with $g=F(f')$ such that $f$ is inverse to $f'$, right? In other words, $F$ is conservative. | |
| Feb 21, 2020 at 3:34 | vote | accept | Jimmy | ||
| Feb 21, 2020 at 3:34 | |||||
| Feb 21, 2020 at 2:34 | history | edited | Pavel Čoupek | CC BY-SA 4.0 |
added 5 characters in body
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| Feb 21, 2020 at 2:23 | history | answered | Pavel Čoupek | CC BY-SA 4.0 |