Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

November 28, 2008

nLab

Posted by Urs Schreiber

After a bit of discussion about going beyond the blog now it is starting to exist: a Wiki accompanying the nn-Café:

nnLab

All there is currently is a welcome message and a faint indication of what should become an index or table of contents. Everybody can work on this, just hit the “edit page” link on the bottom of each page.

We seem to have a slight technical problem with the server that this is running on, as apparently it keeps running out of memory from time to time, in which case the Wiki just hangs and only rebooting the machine seems to help.

So if you work on this now, work in small steps, save frequently, and if the system becomes irresponsive: cry for help. I can reboot the server and Jacques, John and David can.

Let’s use this comment section here to discuss where we are going with this.

Posted at November 28, 2008 4:16 PM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/1862

93 Comments & 0 Trackbacks

Re: nLab

Error 503.

Posted by: Mikael Vejdemo Johansson on November 28, 2008 5:45 PM | Permalink | Reply to this

Re: nLab

Okay, that means I have to reboot. But my train comes in a minute…

I will try to upgrade the server so that this doesn’t happen anymore.

Posted by: Urs Schreiber on November 28, 2008 5:50 PM | Permalink | Reply to this

$15/month

Evidently, 128MB of RAM is insufficient to run a virtual server which does anything nontrivial.

It seems you’ll have to go for the $25/month plan.

Sorry ‘bout that.

Posted by: Jacques Distler on November 28, 2008 8:04 PM | Permalink | PGP Sig | Reply to this

Re: $15/month

I did ask for upgrade. just got an email confirming that now they are charging more. Haven’t had a chance to check if they have upgrded. Am on the train.But site seems to be running.

Posted by: Urs Schreiber on November 28, 2008 8:48 PM | Permalink | Reply to this

Re: $15/month

I’ll help pay — we should pay enough to make this thing work well.

Posted by: John Baez on November 30, 2008 6:55 PM | Permalink | Reply to this

Re: $15/month

It frustrates me that, with literally nothing else running on the server, other than a Mongrel process that occupies 30-40 MB, one can’t comfortably fit within 128 MB.

I know it’s only an extra $10/month, but it’s the principle of the thing!

Posted by: Jacques Distler on November 30, 2008 9:33 PM | Permalink | PGP Sig | Reply to this

Re: $15/month

Just to follow up, since Instiki is the only thing of consequence running on the VPS, and it takes up only 30-40 MB, there’s no good reason why you couldn’t run in 128 MB of RAM.

I consulted with a friend, who’s more of a Linux maven than I am, and he explained why, despite this, so much RAM seems to be in use:

As you can see, literally nothing of consequence, except Mongrel, is running. And yet, “top” reports that there are only 76MB (out of 256MB) free.

top - 21:39:28 up 15:45,  0 users,  load average: 0.00, 0.00, 0.00
Tasks:   1 total,   0 running,   1 sleeping,   0 stopped,   0 zombie
Cpu(s):  0.0%us,  0.0%sy,  0.0%ni, 99.9%id,  0.0%wa,  0.0%hi,  0.0%si,  0.1%st
Mem:    262144k total,   185180k used,    76964k free,    30728k buffers
Swap:   262136k total,        0k used,   262136k free,    80572k cached
PID USER PR NI VIRT RES SHR S %CPU %MEM TIME+ COMMAND 1292 instiki 15 0 45488 40m 3488 S 0 16.0 0:06.86 mongrel_rails

I see what’s going on now (and I’m a little about Linux memory management in the process). It’s mostly going to buffers (30MB) and cache (80MB). Add those up with the 45 MB Mongrel is using and you’re almost to 185 MB. The kernel is apparently trying to make efficient use of the free memory for IO buffers and caching disk blocks for faster access. Unless you’re having some problems, like processes being killed or warnings from the server, then I think everything is okay.

So, y’all could drop back to the $15/month plan, if you want to. Your wiki should work fine. Or you can assume that ncatlab.org will become wildly popular, and you will need the more generous quotas in the $25/month plan.

P.S.: I have backed off to automatically restarting Instiki every 4 hours, instead of every hour. RAM usage is still well within what will fit in 128MB.

Posted by: Jacques Distler on November 30, 2008 11:36 PM | Permalink | PGP Sig | Reply to this

Re: $15/month

I don’t know anything about web stuff, but if it’s genuinely operating system caching (rather than a memory leak from an application) by the linux system (>2.6.16) that’s the problem, running

sync; echo 1 > /proc/sys/vm/drop_caches

will drop anything that’s already on disk from in-memory caches. (The sync makes it write out anything it can to the actual disk first, so more stuff becomes a cache copy of what’s on disk rather than the only version). AIUI there’s no way this command can destroy any data (short of an undiscovered Linux bug that thus hasn’t been fixed yet) so you might want to try this rather than restarting the wiki and see what it does.

However, my (weak) understanding is that Linux ought to detect that it’s caching too much and reduce its caches adaptively so if this does anythgin it’s probably papering over the “real” problem.

Posted by: bane on November 30, 2008 11:51 PM | Permalink | Reply to this

Re: $15/month

I’m just being cautious.

In the original installation, Instiki really was gobbling up all the available memory. Eventually, it would grow so large that the OS would kill it, and the site would go 503.

Having set the permission correctly now, it seems to be behaving correctly, and not gobbling up all the available memory. But (“Once bitten…”) I want to make sure that it’s not leaking memory before I let it run indefinitely (“… twice shy.”).

I’ve set a cron job which restarts Instiki every “n” hours, and records the size to which it has grown before the restart. So far, there’s no sign of a memory leak. When I’m completely satisfied, I’ll get rid of the cron job and let Instiki run indefinitely.

My only observation, so far, is that 128 MB should be plenty sufficient to run this wiki.

Posted by: Jacques Distler on December 1, 2008 12:05 AM | Permalink | PGP Sig | Reply to this

Re: nLab

Thanks a million, Urs!

Posted by: John Baez on November 28, 2008 6:40 PM | Permalink | Reply to this

Re: nLab

‘You must have Javascript on to submit this form.’

The interesting thing is that I do have JavaScript on. Based on past experience, I suspect that what I really need to do is to accept cookies. We’ll see …

Posted by: Toby Bartels on November 28, 2008 9:28 PM | Permalink | Reply to this

Re: nLab

Based on past experience, I suspect that what I really need to do is to accept cookies.

Yep, that was it. So a meaningful error message would be nice. (Especially since I think that more people regularly surf with cookies off than with JavaScript off.)

Posted by: Toby Bartels on November 28, 2008 10:05 PM | Permalink | Reply to this

Re: nLab

My problem is even more curious
sometimes I get the `need to have Javascript on’ but when I try again it’s ok?

Posted by: jim stasheff on November 30, 2008 8:50 PM | Permalink | Reply to this

Cookies

The interesting thing is that I do have JavaScript on. Based on past experience, I suspect that what I really need to do is to accept cookies. We’ll see …

Error message clarified (Revision 277).

Posted by: Jacques Distler on November 30, 2008 11:53 PM | Permalink | PGP Sig | Reply to this

Re: nLab

Oh, so I needed to enable cookies! Now the friggin’ thing finally works! Great!

Someday I want to really explain a lot of math on this Wiki. Having all you friends there will make it a real blast.

Posted by: John Baez on December 1, 2008 1:44 AM | Permalink | Reply to this

Re: nLab

Before you all waste your enthusiasm on error 503, let me try to sort out what’s going on and send a message when things are running stably.

Nothing is ever easy…

Posted by: Urs Schreiber on November 29, 2008 2:16 PM | Permalink | Reply to this

“Easy”

Let me explain what was going wrong with ncatlab.org.

Because of an obscure permissions problem (one that only cropped up when I “upgraded” Instiki to run under the latest Rails 2.2.2), Instiki was falling back to using in-memory caching, instead of the desired file-system caching. This meant that the size of the application would grow over time, eventually exceeding the available memory in the Virtual Private Server (128 MB in the original configuration, 256 MB in the current “enhanced” configuration).

I did two things:
1. I corrected the permissions problem.
2. I’ve set a cron job to restart Instiki once an hour.

Instiki now seems to be occupying at worst ~30–40 MB, after running for an hour, leaving 130 MB free on the VPS.

That’s probably a little too close for comfort to go back to the 128 MB server. But it should be no problem at all in the 256 MB server. If it continues to run stably and not leak memory, I’ll increase (or even eliminate) the time between restarts.

This was much more trouble than I thought it was going to be. But it was very useful for debugging that permissions problem and improving my Linux installation instructions :-).

Posted by: Jacques Distler on November 30, 2008 3:56 PM | Permalink | PGP Sig | Reply to this

Re: nLab

The system seems to work stably now.

I created a couple more placeholder-pages. For instance I started a HowTo page.

As soon as I find the time, I am eager to fill this with proper content.

Posted by: Urs Schreiber on November 30, 2008 8:14 PM | Permalink | Reply to this

Re: nLab

Hi Jacques,

As one of the people who will be using the nLab, I wish to say thanks for all your expert assistance. I am excited to be part of a project which is at the cutting edge of math on the web. To any others listening in: what we do here is important. Jacques’ mathML magic here is part of the data being used by the folks behind Mozila to steer the future of math on the web. So let’s get a good system going!

Urs summarized the difference between the nLab and the n-category cafe as:

You come here to work and go there to chat.

Now the way I see it, if people are going somewhere to work then the ease-of-use of entering math takes on a higher priority (I like the keyboard shortcuts in this regard). I know when I actually want to do some maths, I’m very particular about having the right kind of paper and the right kind of pen!

With this in mind, I have the following questions.

1. I think we badly need to have a “Preview” button when you edit pages… this seems a high priority when one is entering a lot of math.

2. What is the possibility of getting to the point where users can enter their own pre-defined LaTeX macros, definitions, etc.? Can this be handled in the system… even if it means going to javascript? I know there is no concept of a ‘user’ in Instiki at the moment, but perhaps there is some possibility.

Here is a simple system that could work until a more advanced one comes along: just keep a page of site-wide macros, which all the users can edit, eg. containing things like \newcommand\X{\mathcal{X}}. In the edit text for a page, this will appear as \X.

If and when users get added to Instiki, then each user can add their own specific macros, which will get expanded out in the edit text of a page, so as not to cause conflicts. For instance, John Sampson could define his own macro \newcommand\X{\mathfrak{X}}, and then when he types \X on the edit page it will produce a mathfrak{X} in the final HTML. When he edits the page again, he sees \X, but if other users edit the page, they see the expanded macro, i.e. they will see \mathfrak{X}. What do you think?

3. I am very excited by the idea of getting math and SVG to work in a commutative diagrams package. What are your latest ideas on this since you wrote this and this? By the way, I think those diagrams look great… it makes one much more inspired to read a gimungous Urs-style diagram when it comes out nicely like that. This is going to be critical for the nLab.

In order for a command like \mor{ur1}{B}{N BN_B} to place a label on an arrow, foreignObject would need to be able to compute the size of the box containing its content (in this case, “N BN_B”) and, that knowledge in hand, compute its own position relative to the arrow it’s labelling.

Is this still a big stumbling block? Is there any light on the horizon? I’m thinking that if worst comes to worst, surely a javascript solution could work. After all, Davide Cervone must have been performing these kinds of calculations with jsMath.

Perhaps you don’t like a javascript solution, because it seems cludgy. I appreciate that, but it might turn out to work nicely… speed problems shouldn’t be an issue, because there won’t be that many commutative diagrams on a page, even at the nLab.

4. I guess part of what I’m asking for above is how easy it will be for users to develop “plug-ins” for Instiki.

Posted by: Bruce Bartlett on November 30, 2008 7:41 PM | Permalink | Reply to this

Re: nLab

I think we badly need to have a “Preview” button when you edit pages… this seems a high priority when one is entering a lot of math.

Nice, but not really that high a priority.

Just click “Save”. You can re-edit the same page as many times as you like, from the same IP address, within 30 minutes, without each “Save” counting as a separate Revision. Only if you wait for longer than half an hour, or change your IP address, does that generate a new Revision.

What is the possibility of getting to the point where users can enter their own pre-defined LaTeX macros, definitions, etc.?

Macros have been much discussed. There really isn’t a good way to do it within the system (itex2MML + Maruku + Instiki). Javascript is certainly a possibility (and for more than just TeX macros – Keyboard shortcuts, more generally).

All I can say is, if you have a good idea, code it. Instiki is Open Source and, with BZR, everyone can have their own development tree. Mine is here. Its Atom feed (so you can track developments) is here.

Posted by: Jacques Distler on November 30, 2008 9:29 PM | Permalink | PGP Sig | Reply to this

Re: nLab

Currently Chenchang Zhu is visiting for a couple of days and I thought I’d use the opportunity to add a few entries in the nnLab on higher Lie theory.

Doing this, in turn, makes me create entries such as Lie groupoids which in turn makes me create entries such as Internalization.

I quickly filled this with a bit of material off the top of my head, but hopefully you feel sufficiently appalled by these feeble attempts that you can’t help but work on these entries yourself…

Phew, this takes more work than one might think… ;-)

Posted by: Urs Schreiber on December 1, 2008 6:40 PM | Permalink | Reply to this

Case sensitivity

I have little previous experience with wiki-ing, so this may just show my ignorance, but

while working on the Wiki I feel that the fact that page names are case sensitive is becoming a bit of a nuisance.

The page title which is created whenever one types keywords in double square brackets like

[[groupoid]]

etc. appears in two places: as the title of the corresponding page as well as in the URL of that page.

First I paid attention to its appearance in the title and capitalized all words. +

But then, later when one types lots of entries this becomes bothersome: most keywords appear in the middle of the text where one wants them to be lower case, so I want to just tpye [[groupoid]] inline.

But If I previously created a [[Groupoid]] I will have to force lowercase in the running text by typing [[Groupoid|groupoid]].

I know there are worse problems in this world. But

1. Warning: Beware of this fact. It all too easily happens that one links to an entry that in principle exists – but with differently capitalized keyword as title.

2. Question: would it be hard to change this behaviour? I seem to want that typing [[groupoid]] creates and/or links to an entry titled “Groupoid”. (Or maybe I don’t want that. Then please convince me otherwise.)

There is a third thing, which will just show that I nver contributed much to Wikipedia:

what is the caninical choice for singular/plural of keywords? Since I managned to get myself mixed up about this I have now created entries such as Lie groupoids which do nothing but link to Lie groupoid.

Posted by: Urs Schreiber on December 1, 2008 8:45 PM | Permalink | Reply to this

Re: Case sensitivity

Urs is starting to build the nnLab! Watch him work! Or even better, join in!

Urs - are you aiming for a convention where words are not capitalized unless they’re proper names, e.g. ‘Lie theory’?

Wikipedia uses a different convention: the first word in the entry is always capitalized. But, references aren’t case sensitive. So, if you want to refer to the entry on Internalization you can say:

We can define strict Lie 2-algebras using [[internalization]].

I hope there’s a way to achieve this in the nnLab, too. But no matter what, we’ll still need to say things like

We achieve this through [[internalizing|Internalization]] the definition of ‘category’.

In some ways it would be nice to follow a lot of Wikipedia’s conventions, since they have already spent millions of man-hours developing these conventions — and a lot of us know them! They’re also very easy to look up: just go to any Wikipedia page and click ‘edit this page’.

Not all the conventions will apply to the nnLab, but a bunch will.

If we make up new rules, the nnLab should have a page where people can learn the rules we’re making up. For now we can just write a brief note every time we come up against a tricky issue. Writing those notes here is ultimately not as good as writing them in the nnLab itself.

Posted by: John Baez on December 1, 2008 11:41 PM | Permalink | Reply to this

Re: Case sensitivity

I’m not competent enough to write anything meaningful and lasting, but I could probably contribute some material that may need cleaning up later. For example, Urs walked me through many steps of a nice example of groupoidification. I could try to write up my understanding, but would no doubt mess some things up.

Are well-intentioned, if not perfectly correct, contributions welcome?

Posted by: Eric on December 2, 2008 12:06 AM | Permalink | Reply to this

Re: Case sensitivity

Yes, they’re very welcome!

The worst that could happen is that your contributions will annoy someone so much that they replace your entry with a completely rewritten entry that they prefer. Even this counts as progress. But more likely, someone will take your entry and polish it.

This is what happens on Wikipedia all the time.

Unlike Wikipedia, we will eventually set up regions where people can write entries that belong only to them — where it’s impossible or at least strongly discouraged for other people to modify these entries. If you want to write something and not have it overwritten, you’ll be able to do it there.

If anyone wants to do this right now, I suggest that they create a page with their name as the title, and work there until we get a better system.

So far I’ve filled my page with links to some of my papers on higher-dimensional algebra. In the long run, I hope everyone in the world who works on higher-dimensional algebra has a page with links to their papers!

Posted by: John Baez on December 2, 2008 2:19 AM | Permalink | Reply to this

Re: Case sensitivity

we will eventually set up regions where people can write entries that belong only to them

I see you created a “web” John Baez at the nnLab. How did you do that?? :-)

I see a link for editing the web, but not for creating a new one!?

Posted by: Urs Schreiber on December 2, 2008 9:51 AM | Permalink | Reply to this

Re: Case sensitivity

I see a link for editing the web, but not for creating a new one!?

Try clicking on that link.

Posted by: Jacques Distler on December 2, 2008 1:41 PM | Permalink | PGP Sig | Reply to this

Re: Case sensitivity

Try clicking on that link.

Thanks, stupid me.

Posted by: Urs Schreiber on December 2, 2008 2:23 PM | Permalink | Reply to this

Re: Case sensitivity

Hi,

I’m feeling a little guilty about making lots of little notes and minor changes on my page and always seeing it on the top of the list of “Recently Revised” (not to mention what that does to the RSS feed). Would it be possible for me to have a separate “Wiki web” and then when/if I cook up anything worth putting on the official nLab wiki, I can just transfer it over? That would also help me organize my thoughts because right now I have to put all my notes on a single page.

I would also attempt to convince my financial adviser, i.e. boss/wife, to let me contribute a portion of the server fees, which would only make sense. That is trickier then it might seem though after I got myself locked into a gym membership I never use :)

Posted by: Eric on December 29, 2008 4:55 PM | Permalink | Reply to this

Re: Case sensitivity

Eric’s page has:

A Lie ∞-groupoid is supposed to be an ∞-groupoid internal to a suitable category of generalized smooth spaces.

which raises the issue as to whether an $L_\infty$ algebroid is an $\infty$-algebroid in a suitable category of generalized smooth spaces?

i.e does it matter whether `infty’ is attached to Lie or to algbroid?

Posted by: jim stasheff on December 30, 2008 1:19 AM | Permalink | Reply to this

Re: Case sensitivity

Hi Jim,

Just an editorial clarification…

That isn’t my page. My name appears on the bottom simply because I was the last one to modify it. My modification was just a minor cosmetic one. Urs wrote the original statement.

Posted by: Eric on December 30, 2008 4:06 AM | Permalink | Reply to this

C-infinity L-infinity algebroids

which raises the issue as to whether an L L_\infty algebroid is an \infty-algebroid in a suitable category of generalized smooth spaces?

Yes. I am thinking that \infty-Lie theory relates in particular

- \infty-categories internal to generalized smooth spaces (presheaves on CartesianSpacesCartesianSpaces)

with

- DGCADGCAs internal to generalized smooth quantities (co-presheaves on CartesianSpacesCartesianSpaces).

You can find something on this at nnLab/schreiber: generalized smooth L L_\infty-algebroids and section 2.4 of Differential nonabelian cohomology.

Posted by: Urs Schreiber on December 30, 2008 3:38 PM | Permalink | Reply to this

Re: C-infinity L-infinity algebroids

I think both of us are NOT saying fully what we mean or else I’m trying to make a distinction without a difference.

For $L_\infty$- algebroids it is not necessary to be smooth, but even in that case
by $L_\infty$- algebroid do you mean (as I would) a something bundle with an anchor
such that the space of sections forms an
$L_\infty$- algebra?

and is that something bundle a bundle with fibres being $\infty$-vector spaces
i.e. differential graded vector spaces such that…

Posted by: jim stasheff on December 30, 2008 10:22 PM | Permalink | Reply to this

Re: C-infinity L-infinity algebroids

Yes, so ordinarily Lie algebroids are defined in the category of smooth manifolds, smooth fiber bundles.

We want to generalize this to Lie algebroids living in a category of generalized smooth spaces and generalized smooth bundles.

Moreover, we find that in order to describe higher Lie algbroids it is natural not to think in terms of bundles, but entirely in terms of their Grassmann algebras of sections. In terms of these an L L_\infty-algebroid is a DGCA on a GCA free on modules over the ground ring C (X)C^\infty(X).

So to generalize this from XX being a smooth manifold to XX being a generalized smooth space, we need to

1) say what C (X)C^\infty(X) means for a generalized smooth space XX;

2) say what a (graded, projective) module over this thing C (X)C^\infty(X) is.

Moerdijk and Reyes, in their book, do step one and say that what C (X)C^\infty(X) should be: a monoidal co-presheaf on cartesian spaces! See the nnLab entry nnLan: generalized smooth algebra for more details and references.

So the remaining second question is: what is a qDGCA whose underlying GCA is “free over C (X)C^\infty(X)” with C (X)C^\infty(X) such a generalized smooth algebra.

As I said, I think there is a more or less obvious answer.

Posted by: Urs Schreiber on December 31, 2008 11:27 AM | Permalink | Reply to this

Re: C-infinity L-infinity algebroids

we still seem to be 2 ships passing in the night

maybe it would hep to separate to parts of the problem:

the one you care about: what is a qDGCA whose underlying GCA is free over C\infty(X)with C \infty(X) such a generalized smooth algebra.

and the one I care about: what is a qDGCA whose underlying GCA is “free over C ∞(X)” with C ∞(X)= A as in Lie-Rinehart or C ∞(X) = a qDGCA over the ground field
or a qDGA over the ground field (notice: no commutativity)

Now qDGCA says $L_\infty$ without (visibly)
referring to $\infty$-algebroid

Posted by: jim stasheff on January 1, 2009 1:44 AM | Permalink | Reply to this

Re: C-infinity L-infinity algebroids

and the one I care about: what is a qDGCA whose underlying GCA is “free over “C (X)C^\infty(X)” with C (X)=AC^\infty(X) = A as in Lie-Rinehart

Oh, I see. This is (as long as AA is an ordinray associative unital algebra, even though not necessarily commutative) a straightforward generalization of a qDGCA over a commutative algebra of functions. The definition goes through literally, I think, and we get a notion of “L L_\infty-algebroid with a noncommutative space of objects” very naturally.

This is like an \infty-Lie Rinehart pair (A,L)(A,L), where only the Lie part LL of the pair has been \infty-ized, while the associative part AA is kept un \infty-ized.

(As Johannes Huebschmann keeps poiting out to us, he has thought about also \infty-izing the associative part AA here.)

Another generalization which I am interested in better understanding is: keep AA an associative algebra, but allow what used to be a free GCA over it to be not-quite-graded-commutative. I.e.: find the \infty-zation of things like the non-commutative Weil algebra (as described in this blog entry).

By the way, currently Peter Woit is blogging on the n=1n=1-story to be told here. See for instance his slides BRST and Dirac cohomology

Posted by: Urs Schreiber on January 2, 2009 11:29 AM | Permalink | Reply to this

Re: Case sensitivity

Unlike Wikipedia, we will eventually set up regions where people can write entries that belong only to them — where it’s impossible or at least strongly discouraged for other people to modify these entries.

I like this idea. Of course, being a themes man, I propose we establish a different style for these pages (different colours, different fonts for the headers maybe?) via the CSS option. That way one immediately knows which “section” of the nLab one is in.

Posted by: Bruce Bartlett on December 2, 2008 4:03 PM | Permalink | Reply to this

Re: Case sensitivity

I propose we establish a different style for these pages (different colours, different fonts for the headers maybe?) via the CSS option. That way one immediately knows which “section” of the nLab one is in.

Good idea! Let’s do that.

But I need to familiarize myself with how to proceed for this. Maybe you can help me. Do you have some collection of nice themes prepared in the course of your recent investigations into these matters?

Posted by: Urs Schreiber on December 2, 2008 5:07 PM | Permalink | Reply to this

Re: Case sensitivity

Urs, I just “fake it”. To learn how to change the color of something in CSS, I just type “CSS color” into Google and go from there. I see you already have red going in your private pages so you are going strong already. My theme for the n-category cafe, as discussed in this post, is available via Stylish; you can see the code on the page.

A crucial tip with CSS is of course to download the Firebug extension for Firefox. That way, to change the styling of some or other element, you just click on “Inspect” and then click on that element, and you can see all the CSS style-stuff.

Posted by: Bruce Bartlett on December 2, 2008 11:36 PM | Permalink | Reply to this

Re: Case sensitivity

I see you already have red going in your private pages so you are going strong already.

Well. First of all somebody else did that (Jacques I suppose), second: this can be chosen from the Instiki “web preferences” menu. ;-)

Posted by: Urs Schreiber on December 3, 2008 7:28 AM | Permalink | Reply to this

Re: Case sensitivity

How about using something like Redirect to handles the capitalization thing? Is that possible?

For example, could you have the page [[groupoid]] redirect to [[Groupoid]] automatically?

Posted by: Eric on December 2, 2008 12:17 AM | Permalink | Reply to this

Re: Case sensitivity

By the way, I just noticed that the redirect page at wikipedia lists capitalization as one reason to use redirects.

Posted by: Eric on December 2, 2008 12:21 AM | Permalink | Reply to this

Re: Case sensitivity

Yes, Wikipedia uses redirects to deal with capitalization.

There are people interested in math and physics who have spent huge amounts of time working on Wikipedia. Toby Bartels, for example. Others of us have spent time a lot of time designing Eureka.

It would be good to harness the experience of these people, instead of having to rediscover everything.

Posted by: John Baez on December 2, 2008 6:25 AM | Permalink | Reply to this

Re: Case sensitivity

Here is how Wikipedia handles these things:

  1. First, page titles in the MediaWiki software are case-insensitive in the first character. So if you link to [[groupoid]], then it goes to [[Groupoid]]. It’s simply not possible to have a page titled [[groupoid]].

  2. Second, the convention is to use singular names, so the page [[Groupoids]], while possible, really should not exist. If you link to [[groupoid]]s, then the MediaWiki software will automatically put the trailing ‘s’ in the same colour and font as the rest of the link, so the whole thing is transparent to the reader.

  3. Finally, if another name violates the conventions but is convenient to link to, then you create a redirect. So if a lot of people improperly link to [[groupoids]] (which is especially common with irregular plurals), then you can create a page [[Groupoids]] after all but make it redirect to [[Groupoid]] with an entry like #REDIRECT [[Groupoid]]; the MediaWiki software treats a page like that specially.

Notice my references to the MediaWiki software, which after all was developed principally for Wikipedia. For convention #1, this software is essential; for #2, it’s merely cosmetic; for #3, it’s convenient but inessential (saving the reader an extra click).

Another formal convention that I should mention (you can read them all if you like): Page titles are (almost) always nouns. So [[Categorification]], not [[Categorify]] (a verb) or [[Categorified]] (an adjective).

Posted by: Toby Bartels on December 3, 2008 6:05 AM | Permalink | Reply to this

Re: nLab

Now that I worked a bit more on the nnLab a natural question arises:

is there any automated backup process?

Are old copies of that file containing the Wiki’s data being stored for a while?

Posted by: Urs Schreiber on December 1, 2008 10:24 PM | Permalink | Reply to this

Re: nLab

We have plans for 9.99/month that have 256mb ram. IV

Posted by: Adam Stern on December 2, 2008 6:57 AM | Permalink | Reply to this

Re: nLab

Hi Jacques,

Any chance of users being able to replace an uploaded file? I’m wanting such a feature at the moment for CSS, as explained here under Importing CSS, but I’d imagine it could also be important in the future if people start uploading .pdf files of their work to the nnLab, and want to replace them. I guess a copy would have to be kept on the server, else someone could maliciously overwrite someone’s file…?

Posted by: Bruce Bartlett on December 2, 2008 11:56 PM | Permalink | Reply to this

Sacrilege

It is very exciting to see the wiki being born. It is great that a machine has been established to host it. But…

Now that a machine has been established to host a wiki, I humbly submit a suggestion that you also install MediaWiki on it as an experiment.

MediaWiki already has almost every feature you would want to have, plus it is has a very active open source community making improvement that can be incorporated.

If LaTeX support is not suitable enough for your needs, I would submit that we MAKE something suitable. The effort required to develop a suitable LaTeX plugin for MediaWiki would probably be a lot less than the effort to support a proprietary system.

Just a thought, erm, sacrilege…

Posted by: Eric on December 3, 2008 3:43 PM | Permalink | Reply to this

Re: Sacrilege

Hi Eric, I feel your pain :-) The only viable math system for MediaWiki which actually uses text and not images is jsMath. To repeat,as I see it there are only two games in town: jsMath and MathML. To use MathML your webpages have to be “valid XHTML”…whatever that means, it implies that Jacques’ system is the only one on the net!

Now jsMath is cool. It’s very cool. A little bit slow on math-heavy pages according to Jacques, but it doesn’t seem significant to me. So in principle you make a valid suggestion. But I think it’s too late now… running Mediawiki and Instiki side by side would probably chow up that 256Mb the server has, I don’t know.

Jacques’ MathML system is also cool — to my mind the maths comes out very well, maybe even a bit better than with jsMath. And you can change the fonts. And you can integrate with SVG. And you have the advantage of having the web superpowers behind you, because in their infinite (!) wisdom they have decreed that everyone is supposed to use MathML. But then they don’t provide the fonts natively with the browsers. So… they are (insert expletive here).

What features are you talking about? What would you really like to see? Jacques main rationale for choosing Instiki was apparantly that Ruby code is easy to extend, supposedly much better than PHP like Mediawiki.

(But Jacques, it would be nice if you established a well-defined plug-in mechanism whereby people could extend Instiki — like in Mediawiki — without having to “make an entirely new branch”, which discourages development.)

Posted by: Bruce Bartlett on December 3, 2008 9:40 PM | Permalink | Reply to this

Plugins

It’s already there (sort of), albeit undocumented.

Rails allows plugins. See the vendor/plugins directory. Mostly, what’s currently there are packages which I’ve bundled with Instiki, so as to reduce the number of external dependencies.

But, in the past, I’ve had things like the action_cache plugin there, which replaced the (at that time, somewhat rudimentary) Rails caching mechanism with a more sophisticated one.

So it’s certainly possible to extend/replace the functionality of various components of the application by Rails plugins.

But, really, I’m very amenable to incorporating code into the main branch of the application. And by using a DVCS, like BZR, I’ve tried to make it as easy as possible to contribute to the project.

Of course, if — hypothetically — I were to deem your contribution as unsuitable for the main distribution, you could always package it as a Rails plugin.

Posted by: Jacques Distler on December 3, 2008 10:10 PM | Permalink | PGP Sig | Reply to this

MAA Focus

Here is an interesting article (you may have seen it):

Student Collaboration using a LaTeX wiki
Mathematics Association of America, MAA Focus
May/June 2008

I found that via

LaTeX extension for Mediawiki featured in MAA Focus

My thought is that it would be a bigger contribution to the mathematics community to, once and for all, solve the MediaWiki/LaTeX issue since MediaWiki is so pervasive and has such a huge base of support. Putting some of the already existing pieces together, e.g. textogif, etc, I’m sure we could create an extension that would make everyone happy.

I’m only peripherally paying attention to what you guys are doing because things are a bit chaotic in my world at the moment, so apologies if I’m rehashing old settled issues.

Posted by: Eric on December 3, 2008 10:36 PM | Permalink | Reply to this

Re: MAA Focus

My thought is that it would be a bigger contribution to the mathematics community to, once and for all, solve the MediaWiki/LaTeX issue since MediaWiki is so pervasive and has such a huge base of support.

Well as I understand it, jsMath has already solved the MediaWiki/LaTeX issue… as much as that is possible. To my limited knowledge, it is inconceivable that a better solution in Mediawiki could be made than jsMath. That is because jsMath is a stand-alone TeX interpreter, which uses javascript to write out the LaTeX using the Computer Modern fonts. It’s Donald Knuth all over again, in the 21st century.

What better solution with Mediawiki is conceivable? I can’t think of one. Bear in mind that Mediawiki will never be able to run MathML because it “doesn’t validate” (I think… this is true, right?). In a sense this is very sad: the whole strength of Wikipedia, etc. is that it allowed people to come in, write stuff which wasn’t 100% watertight code, but it still displayed it. And that’s why it took off.

But then the web powers started decreeing that “everything has to validate”. And they made it that MathML can only run in such an environment. Which, in my opinion, was a big mistake. Those are the guys who don’t understand how the web works, they don’t realize you need to have some “dirt” in the system to have a productive system. But other people think otherwise.

So now we’re in this situation. Either you use gif files for math, which is what wikipedia does, but I’m sure we’re all agreed that this is not the way for the future. This is essentially the same method Newton used to print the Principia! (except his figures were much higher resolution :-)) So when you say “Putting some of the already existing pieces together, e.g. textogif, etc, I’m sure we could create an extension that would make everyone happy”, I’m a bit confused.

Or you use jsMath. Which is a great solution. But you’re flying in the face of what the Web Powers want us to do. Which I think is actually great, because I think the Web Powers made a big mistake with math, and they ignored the math community (see this document), even though it was theoretical physicists who created the web in the first place! Grr.

So maybe it’s not a bad idea if we say “go jump” to the Web Powers, and we all use jsMath. Sooner or later they’ll listen. But until then we’ll find ourselves alienated from the developments in the Web.

Or we bow down to them, and use MathML. But then we have to use Jacques’ stuff, there’s no other way.

That’s the way I see it.

Posted by: Bruce Bartlett on December 3, 2008 11:49 PM | Permalink | Reply to this

Re: MAA Focus

Bear in mind that Mediawiki will never be able to run MathML because it “doesn’t validate” (I think… this is true, right?)

I was wrong. The Blahtex Mediawiki extension is a LaTeX \rightarrow MathML converter. It looks very interesting. However judging from the page’s history, there doesn’t seem to have been much activity on the project in the last year or so. From one or two of the comments, it seems that they indeed ran into validation issues.

Posted by: Bruce Bartlett on December 4, 2008 12:23 AM | Permalink | Reply to this

Re: conformance

I have some sympathy with Bruce’s frustration, but as someone who used to pretend to follow web accessibility issues and X(HT)ML developments, feel obliged to say that it did arise for a reason. For things non-mathematical I think XHTML and emphasis on validation is a huge improvement over, say, the mid-to-late 1990s… Bruce talks of a little ‘dirt” in the system, but by my recollection things used to be pretty grungy.

I have to admit I’ve never tried to use MathML. Isn’t this the old, old problem of how much syntactic shorthand we want to use? Plus, TeX is at the end of the day a layout engine, and was never intended to mesh with SGML philosophy…

Posted by: Yemon Choi on December 4, 2008 12:25 AM | Permalink | Reply to this

Re: Sacrilege

By the way, using the textogif tool it is quick-n-easy to turn some typesetting-wise heavy duty LaTeX output that goes beyond MathML capacity into a gif and include that as a picture.

Not the optimal solution, but a workable one. See for instance in this nLab entry.

Posted by: Urs Schreiber on December 3, 2008 9:49 PM | Permalink | Reply to this

A Modest Proposal

I’ve been experimenting with the nLab and have to say that I couldn’t think of a better way to do collaborative math. It is fantastic!

I may be retracing a well-trodden trail here, but wanted to say that I think we (mostly you) have an incredible opportunity to make something lasting. The word “Bourbaki” has come up a couple of times already and I think this is potentially nothing less than a new type of Bourbaki.

I am seeing pages pop up containing very tradition terms with very traditional definitions. Can we do better? Should we try?

Given the nature of the n-Category Cafe and its partner nLab, I think it might be worthwhile, if not overly ambitious, to redefine big chunks of mathematics arrow theoretically. What do you think?

Posted by: Eric on December 15, 2008 5:33 PM | Permalink | Reply to this

Re: A Modest Proposal

Here is now a more ambitious view on nnLab:category algebra which provides an “arrow-theoretic” interpretation and indicates a bigger picture lurking in the background.

I have also created a special entry with pointers to Todd Trimble’s discussion of nnLab:ETCS.

I am hoping somebody will find the time to incorporate Todd’s entire marvelous discussion of these category-theoretic foundational issues into the nnLab.

Posted by: Urs Schreiber on December 15, 2008 6:37 PM | Permalink | Reply to this

Re: A Modest Proposal

I’m still a little giddy at how beautiful that is. I sent an email to your google account with a figure that might be useful. I simply redrew the diagram with a 3d perspective. It is a bit of a hack job, but also sent the ppt file.

Posted by: Eric on December 15, 2008 7:29 PM | Permalink | Reply to this

Re: A Modest Proposal

Thanks for the kind words, Urs. This project will keep me busy for a while, and would probably benefit from others’ input.

Ultimately the goal would be to make categorical set theory really easy and user-friendly – something that you don’t have to be an expert in to use readily. But it’s going to take a while before we’re at that point!

Incidentally, this is very much in memory of Saunders Mac Lane. In his last years, categorical set theory was very much on his mind, and he too wanted to make it viable – something you could teach undergraduates. My feeling is that this is indeed possible, but it hasn’t been done yet.

Posted by: Todd Trimble on December 15, 2008 8:07 PM | Permalink | Reply to this

Re: A Modest Proposal

Although I blush at the fact that I haven’t taken a look at the book by Lawvere and Rosebrugh. I really ought to!

Posted by: Todd Trimble on December 15, 2008 8:12 PM | Permalink | Reply to this

Re: A Modest Proposal

Although I blush at the fact that I haven’t taken a look at the book by Lawvere and Rosebrugh. I really ought to!

Yes, you should. Because for a moment I sat here wondering why on earth you thought that this book couldn't be taught to undergraduates. (^_^)

Posted by: Toby Bartels on December 16, 2008 3:08 AM | Permalink | Reply to this

Re: A Modest Proposal

This project will keep me busy for a while, and would probably benefit from others’ input.

In that case, I am wondering if you might be persuaded to develop this project within the nnLab. The kind of activity you are doing is precisely what the wiki was intended for, after all. The advantage over just a series of blog posts (which one can still have of course) is that the material probably becomes more accessible to later readers, that it can be cross-referenced and thus make connections to tons of other things.

As a start, we might just copy your existing entries into the nLab, more or less as they are, and then eventually equip them with hyperlinks etc. If you don’t feel like doing it yourself, maybe you can provide somebody with the source code (I am thinking of all the formulas) to be pasted into some nLab entries.

Posted by: Urs Schreiber on December 15, 2008 8:19 PM | Permalink | Reply to this

Re: A Modest Proposal

I’m happy to supply the source code, but I haven’t been following the discussion about html compatibility and so on. The blog I co-author is a wordpress.com blog, where latexing is done with the latex… between two dollar signs business. So I’m not sure how well that would port to nLab.

Urs, should I email you the html source code I wrote up? Would that work?

Posted by: Todd Trimble on December 15, 2008 8:58 PM | Permalink | Reply to this

Re: A Modest Proposal

In Wordpress (I didn’t realize at first we were talking about entries on your Wordpress blog), there is a way to export all your posts, comments, etc into an XML file. I haven’t tried it, but the output might be convertible to wikitext suitable for nLab. It might require some parsing though.

Posted by: Eric on December 15, 2008 10:28 PM | Permalink | Reply to this

Re: A Modest Proposal

Todd: LaTeX on the nnLab is also done using dollar signs and all that jazz. Just go to any entry and click Edit on the bottom left to see what the source code looks like.

You’ll see some funky html stuff, most of which you probably don’t need to use, but also a bunch of familiar stuff.

If you throw material into the nnLab that’s mathematically interesting but not perfectly formatted, someone will probably come along and polish it up.

We’re waiting for you to join the fun!

Posted by: John Baez on December 16, 2008 1:04 AM | Permalink | Reply to this

Re: A Modest Proposal

Todd kindly sent me the source code of his expositions on ETCS.

I have turned the first of them now into an nnLab-entry nnLab:Trimble on ETCS, I.

This is a simple operation, essentially just copy-and-pasting the code into the nnLab edit window.

Some things to notice are:

1) there is a spam filter active on the nnLab. That complains when one pastes large pieces of text. So I submitted Todd’s story one paragraph at a time.

Strangely, this one sentence here the spam filter didn’t want to accept, no matter what I tried:

On the other hand, set theorists may have greater needs than specialists in the theory of several complex variables

I am not sure which secret message the machine was sensing here…

2) A bunch of formatting issues become easier with the wiki software than with just plain html. For instance:

- Todd used the “blockquote” environment to mimic displayed equations. On the wiki, as on the blog here, one can just use double dollar signs.

- Todd uses “ol” and “ul” environments to produce lists. On the wiki one just types stars or numbers, indented at equal distance, and the software takes care of the desired formatting automatically.

(This is convenient, but also needed: I noticed that MathML math won’t display in an explicit list environment on the wiki.)

I’ll have to do something else now. But if anyone feels like working on this, edit these entries:

nnLab:Trimble on ETCS, II,

nnLab:Trimble on ETCS, III

Posted by: Urs Schreiber on December 16, 2008 12:15 PM | Permalink | Reply to this

Re: A Modest Proposal

I like the idea of just entering unedited pages. That is something even I could help clean up.

Posted by: Eric on December 16, 2008 2:42 PM | Permalink | Reply to this

Re: A Modest Proposal

Gee, thanks a lot, Eric!

Posted by: Todd Trimble on December 16, 2008 4:36 PM | Permalink | Reply to this

Re: A Modest Proposal

Eric now also did part III:

nnLab:Trimble on ETCS III.

Somebody should still go through this and fix/polish here and there.

Posted by: Urs Schreiber on December 16, 2008 9:38 PM | Permalink | Reply to this

Re: A Modest Proposal

Okay, so Eric Forgy kindly did part II: nnLab:Trimble on ETCS, II. That’s great!

I still don’t have time, but if anyone wants to do part III, contact me or Todd for the source code…

Posted by: Urs Schreiber on December 16, 2008 4:41 PM | Permalink | Reply to this

Re: A Modest Proposal

1) there is a spam filter active on the nLab. That complains when one pastes large pieces of text.

No, it complains about certain keywords and phrases. The size of your text doesn’t matter.

Strangely, this one sentence here the spam filter didn’t want to accept, no matter what I tried:

On the other hand, set theorists may have greater needs than specialists in the theory of several complex variables

Hmmm. Beats me.

The list of blocked patterns (RegularExpressions) is here. See if you can figure out which one matched the sentence above.

(This is convenient, but also needed: I noticed that MathML math won’t display in an explicit list environment on the wiki.)

It would be profitable to read the documentation, where the syntax used in Instiki is explained.

  • Not that it’s necessary in this case, but there is an explanation of how to embed Markdown+itex in HTML markup. Generally, Markdown is to be preferred to HTML markup, as the former converts nicely to LaTeX
  • Perhaps it’s a stylistic choice (in which case, feel free to ignore it), but I would have thought that the Theorem Environment would be useful in the nLab. (Again, they convert nicely to LaTeX.)
  • I gather that this page is also of interest to you.
Posted by: Jacques Distler on December 16, 2008 2:51 PM | Permalink | PGP Sig | Reply to this

Re: A Modest Proposal

Thanks, Jacques, that’s helpful.

I added those links explaining

- how to creat definition and theorem environments

- how to upload files

to nnLab:HowTo.

Posted by: Urs Schreiber on December 16, 2008 4:59 PM | Permalink | Reply to this

Re: A Modest Proposal

I just lost about five pargraphs’ worth of work on this page to the spam filter; I have no idea why. As is usual in such situations, I am in no mood to type it all up again. I know that I should save material in an external editor, but that is not how people naturally behave when presented with an edit box. This needs to be fixed.

Posted by: Toby Bartels on December 17, 2008 3:02 AM | Permalink | Reply to this

Re: A Modest Proposal

You found it! Jacques, you're wonderful. And now you can cite a useful feature (or one more useful feature) of Instiki that MediaWiki does not have (at least, it didn't in 2004 …): If an edit is submitted but not accepted, it is still stored on the server. (Probably only temporarily?)

All the same, it would be very nice if, upon rejecting a submission and presenting the user with a new edit box, Instiki would place the rejected submission into the edit box (instead of reloading the source of the current version of the page). Then one could edit it further to remove the spam trigger.

Ideally, it could state exactly what triggered the filter. (But failing that, one could resubmit piecemeal, as Urs did with Todd's ETCS stuff.) That depends on whether you think that spammers will read the failure response or if they're only using bots.

Posted by: Toby Bartels on December 17, 2008 6:07 AM | Permalink | Reply to this

Re: A Modest Proposal

All the same, it would be very nice if, upon rejecting a submission and presenting the user with a new edit box, Instiki would place the rejected submission into the edit box (instead of reloading the source of the current version of the page).

The latest version does that.

(There are some tricky considerations with this, in the case of malicious users who submit invalid utf-8 content, but I think I have that sorted out.)

Then one could edit it further to remove the spam trigger.

I also modified the spam patterns: “cialis” occurs all-too-frequently as a substring in legitimate content.

Posted by: Jacques Distler on December 17, 2008 6:50 AM | Permalink | PGP Sig | Reply to this

Re: A Modest Proposal

All right, now you want something weird? I just did a bunch of edits, originally to ncatlab.org. Then I had to switch computers, typed in the URL, and sent a bunch of edits to www.ncatlab.org. Then if I go to the Recently Revised page at ncatlab.org, it doesn't know about the later edits, although www.ncatlab.org does. If I go to an individual page on ncatlab.org, maybe it knows and maybe it doesn't, while www.ncatlab.org knows them all (I think …). As I go back and forth and force pages to reload, I can watch ncatlab.org slowly discover the changes (still dated over two hours ago) before my eyes! (But there are still a few that it hasn't caught on to yet.)

Probably people testing this should do it in the Sandbox.

Posted by: Toby Bartels on December 17, 2008 11:58 PM | Permalink | Reply to this

Re: A Modest Proposal

Hum, and right now, www.ncatlab.org doesn't know about the most recent edits to [[Eric Forgy]] (which are not by me, but by Eric), although its Recently Revised page does know about them.

Also, I see that ncatlab.org is still slowly learning … the Recently Revised page just caught on, as has [[vector space]]. In fact, John just edited [[vector space]], adding to the material that was only being served from www.ncatlab.org, but only ncatlab.org is aware of this; www.ncatlab.org is not! (Although if I open the edit box, the edit box knows, even though the page itself does not; I guess that this will prevent edit conflicts.)

Posted by: Toby Bartels on December 18, 2008 12:13 AM | Permalink | Reply to this

Re: A Modest Proposal

Posted by: Jacques Distler on December 18, 2008 6:31 PM | Permalink | PGP Sig | Reply to this

Re: A Modest Proposal

Just a quick self-reply to note that I'll be off the Internet for 4 days of vacation. So the n-Lab will have to get along without me. I think that y'all can handle it. (^_^)

(Now if Urs goes on vacation, then we'll have a problem!)

Posted by: Toby Bartels on December 20, 2008 7:05 AM | Permalink | Reply to this

Re: A Modest Proposal

Strangely, this one sentence here the spam filter didn’t want to accept, no matter what I tried:

On the other hand, set theorists may have greater needs than specialists in the theory of several complex variables

I am not sure which secret message the machine was sensing here…

That’s funny. Maybe the spam filter is sensitive to what it perceives as post-modern babblespeak; a lot of mathematics terms (like “several complex variables”) might raise such suspicions. ;-)

Posted by: Todd Trimble on December 16, 2008 4:47 PM | Permalink | Reply to this

Re: A Modest Proposal

Jacques explained the problem: the word “specialists” contains the substring “cialis”.

So, we can’t talk about “specialists” — or for that matter “socialism” — on the nnLab. Which is probably a good thing.

Or at least we couldn’t, ‘til Jacques fixed it.

Posted by: John Baez on December 17, 2008 11:48 PM | Permalink | Reply to this

Re: A Modest Proposal

Ultimately the goal would be to make categorical set theory really easy and user-friendly – something that you don’t have to be an expert in to use readily

I am very interested in this. I feel I want to understand this foundational stuff much better than I do, and that there ought to be a nice picture.

Posted by: Urs Schreiber on December 15, 2008 8:26 PM | Permalink | Reply to this

Re: A Modest Proposal

It would be great to see this develop in the open. I am a good test subject because if I understand it, then anyone could :)

PS: I imagine that an administrator should have the ability to grab the source without Todd having to supply it (?)

Posted by: Eric on December 15, 2008 8:35 PM | Permalink | Reply to this

Re: A Modest Proposal

One thing I’d like to play around with a little more is doing set-theory-like things with string diagrams.

For example, one way of describing a topos is as a regular category (this allows one to do relational calculus, essentially) such that the inclusion

CRel(C),C \to Rel(C),

which takes a “function” f:XYf: X \to Y to its corresponding relation 1,f:XX×Y\langle 1, f \rangle: X \hookrightarrow X \times Y, has a right adjoint. The right adjoint takes a “set” XX to its power set PXP X.

One reason I like this is that we have a kind of string diagram way of representing relational calculus which goes back to C.S. Peirce’s existential graphs, and there should be a nice way of incorporating the adjoint PP into the string diagram picture. Actually, I have a fair amount of backlog material related to this, a lot of it connected to joint work of Gerry Brady and myself. (But I have a terrible track record of getting anything published.)

nLab may eventually be the way to go here!

Posted by: Todd Trimble on December 15, 2008 8:47 PM | Permalink | Reply to this

Re: A Modest Proposal

string diagrams

How do you like to produce these?

The simplest procedure may be that you create the diagrams in your preferred way, store them as gifs or the like on your server and link to them.

The more intrinsic method might be that you use Inkscape or the like and produce the diagrams in .svg format. That may be included directly as source code into nLab entries and thus provides a very robust connection between text and images.

Posted by: Urs Schreiber on December 15, 2008 8:55 PM | Permalink | Reply to this

Re: nLab

How does one delete a page or change the title?

Posted by: Mike Stay on December 18, 2008 7:06 PM | Permalink | Reply to this

Re: nLab

How does one delete a page …

Like this.

… or change the title?

Currently, you can’t. Volunteers to change that are welcome.

Posted by: Jacques Distler on December 18, 2008 7:37 PM | Permalink | PGP Sig | Reply to this

Re: nLab

Hmm. I accidentally created a page “Mike Stay” on your instiki instead of on nLab, and was hoping to be able to fix that; it looks as though one needs the system password to do so, however, so I guess you’ll have to fix it if it bothers you.

Posted by: Mike Stay on December 18, 2008 9:41 PM | Permalink | Reply to this

Re: nLab

As penance, I should demand that you edit one of the contentful pages. Then there would be some point to the existence of your Author Page. :-)

Posted by: Jacques Distler on December 18, 2008 9:46 PM | Permalink | PGP Sig | Reply to this

Accents

Is it possible to make a page title that contains an accent? If so, how? I was hoping to create a page

[[Kähler differential]]

I’m not sure how Wikipedia managed to do it.

Thanks

Posted by: Eric on January 1, 2009 3:53 AM | Permalink | Reply to this

Re: Accents

Unicode WikiLinks work just fine:

[[שנה טובה]]

Posted by: Jacques Distler on January 1, 2009 4:56 AM | Permalink | PGP Sig | Reply to this

Re: Accents

Thanks! After googling “unicode”, I was able to do it by hitting “right Alt+0228” on the number pad.

[[Kähler differential]]

By the way, here is a list of some alt keys for unicode.

Posted by: Eric on January 1, 2009 5:32 AM | Permalink | Reply to this

Re: nLab

I REALLY like what you guys are doing with the nLab. Keep up the good work!

Posted by: Eric on January 9, 2009 7:59 PM | Permalink | Reply to this

Post a New Comment