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created little entries
to go along with the previous entries
(whose $n$Forum-discussion is here)
All of this is part of the cohesion - table.
So whenever we come across a $\mathbf{\Pi}$, we should replace it by ʃ, right? E.g., many in this section.
Maybe for the time being we can just state that ʃ is to be read synonymously with $\mathbf{\Pi}$, with the former potentially preferred in type theory, while the latter potentially preferred from the point of view of algebraic topology.
Did we settle on ʃ? I thought there was some argument that the potential for confusion with an integral sign was undesirable. I kind of like $$$.
You have to decide. To me the similarity of $\prod$ with $\mathbf{\Pi}$ seems to be of the same sort of that of $\int$ with ʃ. I am happy to live with both.
The symbol “$” seems to raise the wrong associations in me, but I guess I can get used to it.
What is not practical for me (if that was suggested above, maybe) is to go and change all the numerous occurences of $\mathbf{\Pi}$ in all $n$Lab entries, all my published articles and all my preprints. Nor does it seem desireable to me.
I am happy with telling the reader at the beginning of each context which notation it should be.
FWIW, I don’t like $ that much, and like the integral-looking thing more (although I don’t know how to type it). I’d always feel $ was some LaTeX typo.
(although I don’t know how to type it)
see here
I’d always feel $ was some LaTeX typo.
Yes, that’s my first association, too. But I suppose I could get used to it.
I think it’s a shame if the use of $ in LaTeX means that we can’t ever also use it in mathematics. LaTeX uses % for comments, but we still feel free to use it for percentages. (-: And it seems unlikely to me that a LaTeX typo would ever actually produce a file which compiled and yet contained some $ characters in the output. But I guess two data points suggests that more other mathematicians would also feel uncomfortable with it.
But is there really an issue with “ʃ” ? To the extent that people think of ʃ$X$ as being “integral over $X$” where $X$ is a type, it actually makes sense: it can be thought of as the homotopy coend over $X$ thought of as a simplicial object. So the only sensible interpretatin of ʃ$X$ as an “integral over $X$” is actually the intended interpretation! So that’s good, not a problem.
I’d think.
If you don’t think there’s a problem with ʃ, I’m okay with it. I guess in other contexts you would be integrating a function rather than a type. Okay, let’s go with ʃ.
Would you object if someone else happened to change $\mathbf{\Pi}$s to ʃs in an nLab page? I’m not planning to go through the whole nLab either, but if I happen to be editing some page anyway, I might want to make it consistent.
Okay, good, yes!
And I am fine with changing $\mathbf{\Pi}$s to ʃ, yes. I just feel overwhelmed with doing it globally and consistently.
(One fine day we might have $n$Lab-wide macros…)
(That would be pretty cool.)
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