Timeline for Two pullback diagram
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22, 2013 at 20:10 | comment | added | Ma Ming | As john pointed, if the category is not a regular category, then one may use the fact that $A\to P$ is a regular epi hence a extremal epi to deduce $B\to P$ is an iso. | |
| Sep 27, 2013 at 21:04 | vote | accept | Ma Ming | ||
| Sep 25, 2013 at 21:03 | comment | added | Ma Ming | Now I get it. By a easy diagram chasing $B\to P$ is a mono, then $A\to B\to P $ is a regular epi, mono factorization of regular epi $A \to P$, so $B\to P$ is a iso. | |
| Sep 25, 2013 at 19:29 | comment | added | Ma Ming | It seems true. Consider the second diagram of mine. $A\to P$ is a regular epi, and the pullback of $B\to P$ along a regular epi is an iso, we want to show $B\to P$ is also an iso. In fact, let $B\to im \to P$ be the image factorization, whose pullback along a regular epi is regular epi + mono, and their composition is an iso, so each of them should be iso. So the problem reduces to when $B\to P$ is regular epi or mono. It is easy for the case mono using factorization property. (not finished for regular epi) | |
| Sep 25, 2013 at 15:59 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 3.0 |