Timeline for Reference request regarding faithfully exact functors between abelian categories
Current License: CC BY-SA 4.0
9 events
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| Jul 24 at 8:10 | comment | added | neander | These are also equivalent to the condition that $F$ reflects epimorphisms, right? I thought it implies 2. as follows. Since $A\to B\to C$ is a complex, we have a monomorphism $Im(A\to B)\to Ker(B\to C)$ in $B$. Carrying these by the exact $F$, we get a monomorphism $Im (F(A)\to F(B))\to Ker(F(B)\to F(C))$, which by the assumption is an isomorphism. Since $F$ reflects epimorphisms, $Im(A\to B)\to Ker(B\to C)$ is also epi, showing the desired exactness. | |
| Feb 22 at 18:55 | history | edited | David White | CC BY-SA 4.0 |
Minor edits; added a tag.
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| Feb 22 at 17:36 | comment | added | David White | I also checked Maclane's book Homology. No luck. | |
| Feb 22 at 17:26 | answer | added | David White | timeline score: 3 | |
| Feb 22 at 17:08 | comment | added | David White | I also checked Buhler's survey on exact categories, Barr's survey, Jack Kelly's recent writings, the stacks project, and [the rising sea][math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf]. Also, the following is relevant to you: math.stackexchange.com/questions/2179003/… | |
| Feb 22 at 16:51 | comment | added | David White | I have been looking for a reference, without any success. I checked Cartan-Eilenberg, Weibel, Freyd's book, and Kashiwara-Schapira. I would encourage you to just write up your own proof and include it as an appendix to your paper. That would be a real service, given how hard it is to find a reference for the result. Also, the following is relevant: math.stackexchange.com/questions/271373/… | |
| Feb 21 at 16:25 | history | edited | Elías Guisado Villalgordo | CC BY-SA 4.0 |
Added reference
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| Feb 21 at 12:22 | history | edited | gmvh |
Added top-level tag
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| Feb 21 at 10:35 | history | asked | Elías Guisado Villalgordo | CC BY-SA 4.0 |