Timeline for Two pullback diagram
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2013 at 17:47 | answer | added | Michal R. Przybylek | timeline score: 13 | |
| Sep 29, 2013 at 22:12 | comment | added | Ma Ming | @MichalR.Przybylek Sure, any further elaboration is welcomed. My connection is super bad these days, sorry for later reply. | |
| Sep 27, 2013 at 21:12 | comment | added | Michal R. Przybylek | @MaMing, I started writing an answer based on the above comment, but now I see that you've already accepted one of the answers given so far. Does it mean that you are completely satisfied with the answer and not interested in any further elaboration? | |
| Sep 27, 2013 at 21:04 | vote | accept | Ma Ming | ||
| Sep 26, 2013 at 20:25 | answer | added | john | timeline score: 5 | |
| Sep 26, 2013 at 15:34 | comment | added | Michal R. Przybylek | My initial guess is that your condition is equivalent to the condition that the pullback functor along $X \rightarrow Y$ is conservative. The pullback functor is conservative if the mediating maps are strong epimorphisms (in fact, up to some mild assumptions on the category, the converse is true as well). If my guess is correct, then this explains the case of regular categories --- since in a regular category regular epis coincide with strong epis and are stable under pullbacks. | |
| Sep 25, 2013 at 15:59 | answer | added | Peter LeFanu Lumsdaine | timeline score: 9 | |
| Sep 25, 2013 at 9:04 | history | edited | Ma Ming | CC BY-SA 3.0 |
added 3 characters in body
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| Sep 25, 2013 at 8:59 | history | edited | Ma Ming | CC BY-SA 3.0 |
added 3 characters in body
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| Sep 25, 2013 at 8:54 | comment | added | Andrej Bauer | In sets every epi splits. I have a feeling it might help to know that $X \to Y$ is a split epi, not just epi. | |
| Sep 25, 2013 at 8:38 | history | edited | Ma Ming | CC BY-SA 3.0 |
added 3 characters in body
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| Sep 25, 2013 at 8:22 | comment | added | Martin Brandenburg | @Ma Ming: Can you add your proof for the category of sets when $X \to Y$ is epi? | |
| Sep 24, 2013 at 18:30 | answer | added | Eric Wofsey | timeline score: 5 | |
| Sep 24, 2013 at 18:19 | comment | added | Andrej Bauer | I can't tell immediately whether this is research-level. Therefore it probably is. Hmm, but only assuming I actually know anyhing about category theory. The dilemma is unbearable. | |
| Sep 24, 2013 at 17:47 | history | asked | Ma Ming | CC BY-SA 3.0 |