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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 14th 2010

I tried to structure the entry Heyting algebra a bit more. Check if you like it.

I also added a little bit to the Examples-section.

In the section on toposes it says that a “Grothendieck (0,1)-topos” is a locale. Is that correct? Shouldn’t it say: a Grothendieck (0,1)-topos is a category of open subsets of a topological space?

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeDec 14th 2010

The entry looks good.

Shouldn’t it say: a Grothendieck (0,1)-topos is a category of open subsets of a topological space?

Why do you say that? Just like a Grothendieck 1-topos need not have enough points, a (0,1)-topos need not either.

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeDec 14th 2010

OK, I can vaguely see the point of all those Definition boxes, especially if we were later to put in proofs for the equivalences between them, but is there a reason for separating out Remarks like that? Is there no room for a paragraph that just stands on its own?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeDec 14th 2010
• (edited Dec 14th 2010)

Why do you say that?

Sorry, that was nonsense. Not sure why I said that.

is there a reason for separating out Remarks like that?

I like it. It helps me scan the entry very quickly for information. But feel free to delete the remark-environments again, or some of them, if you feel that’s better.

• CommentRowNumber5.
• CommentAuthorTobyBartels
• CommentTimeDec 15th 2010

I’ve never liked Remark environments in books; Definition/Theorem/Proof are formal but remarks are not, so Remark environments only make sense to me in books (like Walter Rudin’s) where every paragraph is numbered and you want a word to stick in front of the number when citing it. After our discussion about the proof environment at Eckmann-Hilton argument, I was afraid that you wanted these too. But since you write

feel free to delete the remark-environments again, or some of them

I don’t feel threatened that the Lab will become as ugly as all that. (^_^)

• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeDec 15th 2010

I think Remark environments make sense when (1) you want to refer back to the remark later (“see Remark 4.3”) or (2) you want a paragraph or a group of paragraphs to be “set apart” from the rest of the text as a sort of “side comment,” so that upon encountering the line space after the remark-environment the reader thinks “okay, that digression is over, now back to the main development.”

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeDec 15th 2010

My only aim is to make the nLab a useful source of information. Useful for me also means that I can extract information from an entry efficiently and quickly – – say when having a quick glance at an entry while in the middle of the discussion with somebody else. For that i want to have it a structure as clear as possible.

We have or had a bunch of entries that were not structured very well. One had to read the whole entry carefully line by line to get the relevant information. For instance there were some tendencies to write historical or terminological remarks before the definition was even stated, to intersperse the definition with plenty of paranthetical remarks or with examples or consequences before it was even fully stated, and things like that. I tried and will continuously try to restructure such entries, to make them more efficiently readible, will move historical remarks to the end of the entry, will try to separate clearly definitions from side remarks from examples, etc.

In my attempts to add structure to entries, maybe I am overshooting here and there and adding too much structure. Since I am not dogmatic about any of this but just want to have useful entries, you should all feel free to in turn polish my edits if you find them misguided.

• CommentRowNumber8.
• CommentAuthorTobyBartels
• CommentTimeDec 15th 2010
• (edited Dec 15th 2010)

I agree that the organisation of entries is often bad, (although of course this is better than no entry at all).

If a remark is truly an aside, then it probably belongs in a different place. I’ve done this with half of one remark, which began “for example” (and also added to it). The rest of that remark, however, seems to me part of the main development of the definition, so I removed it from the Remark environment. Another Remark environment remains.

• CommentRowNumber9.
• CommentAuthorzskoda
• CommentTimeDec 15th 2010

Urs, the thing which I do not like about structuring is that the entries grow with all the extra data, extra tables, extra titles, extra fonts, extra boxes etc. I myself remember things very visualy and the shorter is the text i comprehend and remember it better, after I understand it once. So in conclusion I like the structure and levels of strcuture when an entry grows already big before blwing it additionally. But for small entries which have 2-3 paragraphs and where the visual memory and visual comprehension works best, I am irritated when it becomes full of tables.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeDec 15th 2010

So in conclusion I like the structure and levels of strcuture when an entry grows already big before blwing it additionally. But for small entries which have 2-3 paragraphs and where the visual memory and visual comprehension works best, I am irritated when it becomes full of tables.

We can do something about this: expand these short entries! ;-)

(The thing is if you create an entry that is still very short, I will add the TOC immediately so that it is there later when the entry grows bigger. For if I don’t do it immediately, I will forget to do it. And since many of you don’t do it, nobody would.)

• CommentRowNumber11.
• CommentAuthorTobyBartels
• CommentTimeDec 15th 2010

And since many of you don’t [add the TOC], nobody would.

I’m now good at adding the TOC, so that I get a chance to add it the right way rather than Urs’s wrong way. (We don’t change each other’s versions.) Without Urs to spur me, I might forget!

• CommentRowNumber12.
• CommentAuthorMike Shulman
• CommentTimeDec 15th 2010

I agree with Zoran that there is an advantage to shorter things; it’s easier for me to “grok” a page, or a section of a page, if it doesn’t require lots of scrolling up and down (or even left and right!) to read. For this reason I sometimes change displayed equations to inline ones, if they are small, and collapse bulleted/numbered lists into a paragraph.

For instance, if a definition has only two fairly short conditions, I think it is easier to read in a paragraph rather than in a numbered list. I think lists are only helpful when they contain at least three entries, and often three or even four conditions can be more easily grasped when described in a paragraph.

I’m not against organization/structure as such, but I think the point is not to let the structure overshadow the content.

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeDec 17th 2010

Okay. I get the point.

• CommentRowNumber14.
• CommentAuthorTobyBartels
• CommentTimeDec 17th 2010

In contrast to Mike, I’ve come to like spread out white space and bulleted lists after seeing Urs’s usage of them! I use the latter a lot more now, even in simple emails.

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeDec 17th 2010

Okay, that’s useful to know, too! :-)

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