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    • CommentRowNumber1.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    Over at Theta category, we have an idea section but no definition. Could someone add it in at some point? I understand the need for an idea section, but don't you think that a definition section is equally important?

    (I'd add it myself, but I don't know the definition!)

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010

    but don’t you think that a definition section is equally important?

    I think it’s important!

    Who of you all forgot to put it in?

    • CommentRowNumber3.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010

    Apparently you =).

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    Apparently you =).

    No, why? If nobody does it, why is it my fault? Because I put in the Idea? If I put in the idea, and you do nothing, why do you complain to me that I didn’t put in more? I should to complain to you that you didn’t do anything!

    If you see what I mean.

    If I want to put something on the nLab, I will not hesitate to do it, just because it might not be a fully comprehensive discussion in the first go.

    • CommentRowNumber5.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    Speaking of which, I would argue that maybe putting the abstract definitions first on pages could be useful. It's often very easy for people to get caught up in writing about the idea while totally forgetting to write down a definition. I find it particularly useful to have the formal definition first, then the idea or motivation section to "help me digest the definition", so to speak. Often, this encourages the writer to give an explanation of the definition rather than a vague "idea" of what's going on. I find the "why does this definition make sense of our intuitions" much more helpful than the "what we are about to define is crazy awesome".

    Edit:

    @Urs: No need to get defensive. I was joking! That's why I put a smily face. I appreciate the amount of time you spend writing for the nLab. =) (not joking this time though!)

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010

    No need to get defensive. I was joking!

    I was joking, too. I thought you didn’t get my joke. That’s how it goes on the web.

    I was trying to ironically point out that a question like your “doesn’t anyone thing this should be improved” always have a standard answer. Nobody leaves an page imperfect due to a desire to have an imperfect page.

    Concerning the order: sure, if giving the definition first helps. Whatever helps is allowed. I think back then we had discussion that some entries started out too heavy on the machinery, and that these should be preceded by a more gentle introduction.

    Whatever works. That’s why I, personally, think that the automatic TOC is important: it allows the reader to individually decide which parts of the entry are of interest to him. Or her.

    • CommentRowNumber7.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010

    I have a kinda neat idea for the nLab that wouldn't require very many changes.

    Have something at the (top, bottom?) of each page called "ingredients", "prerequisites", or "stuff you need to understand before reading this one".

    I was also thinking that maybe splitting some of the (∞,1) stuff out into separate articles could make it easier to follow. This would also make the nLab easier to "learn from" rather than "look things up in".

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010

    Have something at the (top, bottom?) of each page called “ingredients”, “prerequisites”, or “stuff you need to understand before reading this one”.

    Isn’t that what the hyperlinks achieve? Whenever you come across any technical term, it should be a hyperlink. You decide then if you know the term already and keep on reading, or if you need more background, in which case you follow the hyperlink.

    I was also thinking that maybe splitting some of the (∞,1) stuff out into separate articles could make it easier to follow.

    I don’t know what to do with this suggestion. But if you have concrete suggestions for concrete pages, concerning improvement, I’d be happy to hear them.

    • CommentRowNumber9.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    @Urs: I'm saying that these are things that I'm planning to do, not things that I'm requesting that you do.

    Also, with respect to the first suggestion, no. The hyperlinks are totally useless for that. I'm saying this as someone who has tried with a reasonable amount of vigour to learn mathematics from wikipedia or the nLab. There's definitely something to be said for having at least a suggested linear ordering on the pages. The problem with hyperlinks is that it's often very hard to tell which ideas are important and which ideas are of little to no consequence.

    For the second suggestion, this is something that I'll do by myself (of course, I'll leave a note on the forum every time I do it, so if you have any objections, there will be sufficient time to voice them before I go ahead and move them).

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    Harry,

    if you have a suggestion, the fact that you have come up with it means that chances are you are already the most expert person for that suggestion. For instance when you read a page and think “Darn, those hyperlinks don’t help me at all, but if I had only been told from the very beginning that I would have to read precisely entries A, B and C, then that would have been helpful”. In such a case, by all means, add a sentence to the beginning of the article giving that information.

    I wish we’d spend less bandwidth on the forum with should one/could one discussion and more on the nLab with just doing it, as long as it is not going to be controversial. (And even then, but then mark it as such.)

    • CommentRowNumber11.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010

    Yes! This is precisely my plan. Give me roughly two weeks and this is what I intend to start doing! The problem is that right now, I don't have time to learn the ins and outs of the instiki syntax.

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010

    Yes! This is precisely my plan. Give me roughly two weeks and this is what I intend to start doing!

    Right. There is something I should say in reply to this. But not right now, maybe in a month. I am too busy writing forum messages at the moment.

    The problem is that right now, I don’t have time to learn the ins and outs of the instiki syntax.

    Now you are joking again, I hope.

    • CommentRowNumber13.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010

    I've got final exams and other work to do =p.

    • CommentRowNumber14.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    I put down a formal definition of Θ\Theta at Theta category.

    If the formal definition is hard to grok, then I recommend looking at the guidebook by Cheng and Lauda, in the chapter titled “Joyal”.

    • CommentRowNumber15.
    • CommentAuthorAndrew Stacey
    • CommentTimeApr 14th 2010

    I've got final exams

    And the rest of us have to write the exams!

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010

    Except for me. I am just sitting here all day waiting for Harry to announce a suggestion (in two weeks) about adding some hyperlink to some entry. ;-)

    • CommentRowNumber17.
    • CommentAuthorHarry Gindi
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    Ouch.

    You wound me, sir.

    The post on the nforum would be for splitting the (infinity,1) case and the ordinary case. I have no qualms about just adding links =p.

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    I put down a formal definition of Θ\Theta at Theta category.

    Thanks, Todd. I added some links.

    Your very first sentence in the definition section speaks of “the free ω\omega-category on the terminal globular set”. Wouldn’t that be the terminal omega-category? Is this really what you meant to say? (Maybe I am too tired.)

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010

    The post on the nforum would be for splitting the (infinity,1) case and the ordinary case.

    Ah, I didn’t get that. I only understood that you suggested to spearate some unspecified entries into some other unspecified entries.

    Yeah, I keep changing my mind about what to do about these cases.

    • CommentRowNumber20.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 14th 2010
    • (edited Apr 14th 2010)

    I think I meant what I said: I was referring to the functor T:Set Globe opωCatT: Set^{Globe^{op}} \to \omega-Cat which is left adjoint to the underlying functor. Of course, the terminal globular set carries a unique structure of ω\omega-category, and that will be the terminal ω\omega-category, so I don’t think there’s much chance of confusion.

    Edit: Maybe I misunderstood what you were asking. So here’s an answer to what you might have asked: no, the free ω\omega-category on the terminal globular set is not terminal. For example, the free category on the terminal directed graph (which has one vertex and one edge, which is a loop) is the… well, you know what it is, and it’s not terminal.

    • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010
    • (edited Apr 15th 2010)

    Ah, thanks, Todd. See, I was mixed up. I didn’t realize that the terminal directed graph does have an edge, of course. I was just visualizing a point and not thinking. Right, sorry, stupid me. But i’ll add a remark on that into the entry.

    • CommentRowNumber22.
    • CommentAuthorUrs
    • CommentTimeApr 14th 2010

    I added accordingly a sentence to Theta category at the beginning of the Definition-section.