Timeline for Why is $Lex(\mathcal{A},\mathcal{Ab})$ abelian? Does $Lex(\mathcal{A},\mathcal{Ab})\rightarrow Func(\mathcal{A},\mathcal{Ab})$ admit a left-adjoint?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 28, 2013 at 22:33 | comment | added | archipelago | Yes, the class of epimorphisms in an abelian categroy forms a site and the sheaves of abelian groups on site site are exactly the left exact functors. Gabriel's elementary constructed left adjoint I mentioned in my answer then corresponds to the abstractly constructed sheafification-functor. | |
| Oct 24, 2013 at 9:34 | comment | added | Matthias Künzer | Laumon (MR0726427) interpretes Lex as a category of sheaves on a site - whence it is abelian. The proof in Gabriel's dissertation I couldn't entirely follow. | |
| Oct 3, 2013 at 2:00 | answer | added | Samantha Y | timeline score: 4 | |
| May 11, 2013 at 17:55 | comment | added | archipelago | Isn't this notation quite common? $Lex(A,B)$ denotes the category of all left−exact functors from $\mathcal{A}$ to $\mathcal{B}$ and $Func(\mathcal{A},\mathcal{B})$ the category of all functors. | |
| May 11, 2013 at 17:45 | comment | added | Fernando Muro | It would be helpful that you explained the notation you're using. | |
| May 11, 2013 at 16:18 | answer | added | archipelago | timeline score: 6 | |
| May 11, 2013 at 14:25 | history | asked | Kathrin | CC BY-SA 3.0 |