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I am starting salamander lemma
I tried to rename the page titled “Anton Greschenko” to “Anton Geraschenko”, apparently without success (?). I was hoping that when I clicked on Anton Greschenko in salamander lemma, I would get redirected to the renamed page, but I got sent to Anton Greschenko instead. Cache bug problem, where I now cannot edit Anton Greschenko (I get sent to the home page).
We really need to have some clear instructions on how to fix such things without creating cache bugs.
Sorry for the typo. Thanks for catching it.
I have fixed it at salamander lemma. Now the ill-spelled entry is no longer linked to, and should not be a source of worry.
I have been expanding salamander lemma. My goal is to have the main statements and corollaries of Bergman’s aricle reproduced there, together with proofs that pedagogically spell out also little steps, such as to make the whole thing useful for novices.
But I have been working on this page less enthusiastically than I should, and so it remains under construction for the moment and will have to be completed a little later this week.
Perhaps someone can check this out but I think there was a closely related result in one of Ross Street’s early papers. Here it is: Homotopy classification of filtered complexes, J. Australian Math. Soc. 15 (1973) 298-318; MR49#5135.
This was extracted from his thesis. I expect that George Bergman’s result is not in there but there may be other stuff of use/interest.
Here it is: Homotopy classification of filtered complexes, J. Australian Math. Soc. 15 (1973) 298-318; MR49#5135.
Thanks. I have now put this into filtered chain complex.
Have been further working on the entry salamander lemma.
Now the entry has pretty much everything from the first two sections of Bergman’s article, including the relevant pictures of long diagonal zig-zags.
I’ll go through it a bit more, but for the moment I need a break.
added the proof of the four lemma at salamander lemma - implications - four lemma.
I have been adding a fair bit of further details to the section The salamander lemma. I spelled out all the proofs of all those little statements involved in full explicit detail (referring to elements in modules). Of course all these proofs are immediate, but I have a certain audience in mind who will appreciate that level of detail.
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