Timeline for Snake lemma for equivalence relation
Current License: CC BY-SA 3.0
13 events
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| Feb 7, 2018 at 14:25 | comment | added | Ivan Di Liberti | @KevinCarlson, on one hand you must be right. On the other, one can prove that when $g_i$ is a regular epi for all $i$ then the sequence $E(g_1) \rightrightarrows E(g_2) \to E(g_3)$ is exact (At least, I think I proved it). This kind of motivates me in the direction that something should be true. In this spirit I asked the following question: math.stackexchange.com/questions/2629757/… But still, the subject is cloudy to me and I do believe you are right. | |
| Feb 7, 2018 at 6:03 | comment | added | Kevin Carlson | I would go to the original reference for Barr-exact categories, with the warning that you shouldn't expect to do homology theory in an exact (let alone regular) category. There's a reason Borceux-Bourn called them homological categories. In particular, I don't see how one would hope to define $E(\nu)/E(f)$ without being in a pointed category, and realistically much more than that. Here's Barr's original, if you can pass Springer's paywall: link.springer.com/content/pdf/10.1007%2FBFb0058580.pdf | |
| Feb 2, 2018 at 10:37 | comment | added | Ivan Di Liberti | No, in general it is not. $g_3$ must be al least surjective to be so. | |
| Feb 2, 2018 at 0:40 | comment | added | Gerrit Begher | Is $E(g_3)\to ... \to Z$ always exact? | |
| Jan 30, 2018 at 10:07 | comment | added | Ivan Di Liberti | That is a very good question, I spent the whole yesterday trying to do so. Still I am trying. | |
| Jan 30, 2018 at 10:06 | comment | added | Arnaud D. | How do you define $E(v)/E(f)$? | |
| Jan 29, 2018 at 18:52 | history | edited | Ivan Di Liberti | CC BY-SA 3.0 |
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| Jan 29, 2018 at 18:22 | comment | added | Yemon Choi | I feared as much. In that case I do not know of a suitable reference. Perhaps you could ask on the category theory mailing list? | |
| Jan 29, 2018 at 16:56 | history | edited | Ivan Di Liberti | CC BY-SA 3.0 |
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| Jan 29, 2018 at 16:51 | comment | added | Ivan Di Liberti | I will give a better look to the book but the hypothesis of Malcev is way too strong for me. | |
| Jan 29, 2018 at 16:47 | comment | added | Ivan Di Liberti | Yes it is, thanks for the reference. I will give a look. | |
| Jan 29, 2018 at 16:46 | comment | added | Yemon Choi | This sounds like the sort of thing that might be in the book of Borceux and Bourn, but perhaps they start by imposing further conditions on your category that are too restrictive for your purposes. (That said, one of their main aims is to work with good categories that are not additive; is this the kind of thing you want?) | |
| Jan 29, 2018 at 16:42 | history | asked | Ivan Di Liberti | CC BY-SA 3.0 |