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Every single spectral sequence I have seen in my life was denoted by $E$. Even when there is more than one spectral sequence, people tend to use the same letter with some workaround (e.g. a fourth subscript on the left).
Why don't we open our mind and start to use the letters we like more (like the initial of the guy that gives the name to the spectral sequence)?
My real question is: are there good reasons to continue using $E$, or can I use different letters? Do you think I will be asked to change it back to $E$ by reviewers?
$\begingroup$Probably because everybody knows what it is. You are of course welcome to use whatever notation you like; but your main job is to communicate your ideas clearly to other readers. Unless a notation is obviously better most people wouldn't bother to change the way they write things. Many times I have read older manuscripts where the author took an "artistic decision" with the notation; and it has left me pointlessly confused in most cases. I think that in homological algebra the letters A,B, C and D are often used for modules and E is typically "different enough" to not be confusing.$\endgroup$
$\begingroup$While I understand your frustration, perhaps some counter-questions are in order: are there good reasons to always use $d$ for the boundary map? To always use $\int$ for an integral? To always use $\pi$ for the ratio of a circle's circumference to its diameter? Why is the existing notation not good? Are there good reasons to change it to something new instead of leaving it in place? Sometimes when we "open our minds" too much, our brains fall out, and it is better to leave those in place, at least :-)$\endgroup$
$\begingroup$@Carl-FredrikNybergBrodda: not sure I got your point. Things you are citing have a fixed meaning, and I am okay with that. Thing here is that we have a whole category of spectral sequences, and just one letter to denote them. Since spectral sequences comes with three sub/super-scripts, it's not even wise to use other sub/super-scripts to distinguish them. So if I have more than one spectral sequence, I have to use a messy notation like $E^{p,q}_r(G)$ (where $G$ for example stands for Grothendieck) or ${}_1E^{p,q}_r, {}_2 E^{p,q}_r, {}_3 E^{p,q}_r$..$\endgroup$
$\begingroup$@AndreaMarino: The notation like $E^{p,q}_r(G)$ never seems too bad for me. Formally, it’s well-justified by viewing $G$ as the abstract spectral sequence, and $E^{p,q}_r$ as the functors extracting the components. Pragmatically, its advantage over, say, $G^{p,q}_r$ (which I guess is what you would advocate?) is that the $E$ clearly distinguish it as a spectral sequence, and distinguish the components themselves from the various other objects associated to the sequence (e.g. homology groups, etc.).$\endgroup$
