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Under definition 1 of salamander lemma, I fixed a mistake in the definition of $A_\Box$ where there was a direct sum of two submodules, where there needed to be a sum (i.e., join) instead.
Thanks for catching this.
And thanks for looking into writing out a proof of the braid lemma, if I am guessing correctly that this is what you are doing?! :-)
I hope to be doing that, yes; it may take a little while because I’ve never looked carefully at the salamander lemma – I’ve only had an idea what it was good for.
Also in salamander lemma, looking at the zig-zags after remark 3, they look off. The \swarrows should pertain to vertical differentials according to 2. under remark 3, but in the zig-zags below the \swarrows go from $X_{k+1,l}_\Box$ to $^\Box X_{k, l}$, i.e., an extramural map corresponding to a horizontal differential $X_{k+1, l} \to X_{k, l}$. So I assume the arrows in both zig-zags should be switched to the opposite directions.
Thanks, Todd. Right now I don’t have the leisure to check. I could check later today. But if you looked at it and think it’s a typo, I suppose you should feel free to fix it.
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