Timeline for Pullbacks of Abelian Categories and their Ext-Groups
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2012 at 21:10 | comment | added | Lennart Meier | @Theo: What they do, seems to be slightly different. @Martin: Yes, F and G should be exact. For the case of quasi-coherent modules on an open covering it works. | |
| Jul 22, 2011 at 20:13 | comment | added | Martin Brandenburg | Also, have you checked the example that $F,G$ are restriction functors from quasi-coherent modules along open subsets? | |
| Jul 22, 2011 at 20:10 | comment | added | Martin Brandenburg | Lennart, do you assume that $F,G$ are exact? Otherwise $A \times_C B$ has no chance to be abelian. | |
| Jul 22, 2011 at 18:07 | comment | added | Theo Buehler | It looks a bit like you want to "glue" stuff together. If so, then this paper by Polishchuk (and the references thereein) seems relevant: arxiv.org/abs/math/9811155 In the introduction it is stated that the gluing need not necessarily be of finite cohomological dimension even if the original categories are of finite cohomological dimension (I haven't looked very closely, though). | |
| Jul 22, 2011 at 16:22 | history | asked | Lennart Meier | CC BY-SA 3.0 |