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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 21st 2009
• (edited Dec 21st 2009)
This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>Probably most contributors here have subscribed to the category theory mailing list. For those who have not, this is to point out that lately the nLab keeps being mentioned there again and again with positve connotation.</p> <p>Most recently, Andre Joyal, not the least among category theorists, to put it in an understatement, wrote:</p> <blockquote> The n-category caffé is an extraordinary experiment in research collaboration and dissimination of knowledge. It maybe the way of the future. But an old mathematicians like me find it difficult to adapt to this new form of collaboration. </blockquote> <p>He mentions the blog here, but previously he had linked extensively to the lab.</p> </div>
• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeDec 28th 2009

Maybe he is a bit afraid of producing the wiki source code. As it is not just text or LaTeX and has all the brackets etc. for links and other special effects, it may be looking tricky, many people are afraid of such first steps and all the sorrounding slang like licenses, nPOV-s, markups, ruby on the rails, export, latest changes, "evil", red herring etc. to name few assumed notions which the colleagues from my institute would not understand.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeDec 29th 2009
• (edited Dec 29th 2009)

I am having a discussion with Andre Joyal, partly on the CatTheory mailing list, on this (as you have seen).

He says that might want a separate wiki on "category theory" and indicates that it is the statement on the HomePage and similar, that makes it sound to him as if we take higher category theory to be more fundamental than category theory, while he feels it is the other way round, and that this makes him want a separate category theory wiki.

In reply I now said two things:

• that, despite the way we may have phrased it, we don't really think of the nLab as preferring higher cateory theory over category theory. Each applies where applicable.

• that, be that as it may, if he tells me that he would start adding content to a instiki-web titled "category theory" rather than to the nLab proper, then, being the highly esteemed potential contributor that he is, we'd be glad to create such a web for him, anyway.

• CommentRowNumber4.
• CommentAuthorEric
• CommentTimeDec 29th 2009
My suggestion is to think of a name and create a new wikiweb dedicated to category theory. How about "CatTheory" just as in the mailing list in an attempt to attract that established community?
• CommentRowNumber5.
• CommentAuthorzskoda
• CommentTimeDec 29th 2009
• (edited Dec 29th 2009)

I disagree with Joyal about the assertion that quantum groups have no applications in physics. It seems he is not interested in integrable models, hidden symmetries of CFT, group theoretic model building and alike where quantum groups are important, and also the harmonic analysis on quantum groups and special functions related to quantum groups. However I agree with him in a modified statament: I know of almost no applications of generic quantum groups in physics, only root-of-unity quantum groups have significant applications so far.

I agree with Urs's response a lot. Having Prof. Joyal a contributor would be gain for the nlab and humanity.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeDec 29th 2009

Maybe we should just go ahead, create that web, and then see what happens.

Andrew, Toby, could one of you create a sub-web titled "category theory"? (I don't think I can do it at the moment, can I?) Then I'll email Andre Joyal the URL.

• CommentRowNumber7.
• CommentAuthorzskoda
• CommentTimeDec 29th 2009

Of course, once he starts working in it and linking to main nlab entries he will judge more easily if it is beneficial to his style to unify the effort or unify part of the effort.

• CommentRowNumber8.
• CommentAuthorTobyBartels
• CommentTimeDec 30th 2009

If we have to create a new web to get him to contribute, OK, but I'm probably going to want to copy everything that he writes over to the main web. So it would really be much more efficient if we can convince him to contribute to the main web.

A Joyal personal web might also be a good offer, but different from what's being discussed here.

• CommentRowNumber9.
• CommentAuthorMike Shulman
• CommentTimeDec 30th 2009

I'm with Toby. I really really don't want there to be a separate "category theory" web. There is so much category theory already on the nlab. One of the great benefits of the nlab is having one place for all of this information. I view higher category theory as one subject within category theory, and I myself do both higher category theory and other kinds of category theory, and I would really hate to have to think about which web a given subject should go on. Can't we just change the intro and about pages somehow to make it sound more inviting to non-higher category theorists?

• CommentRowNumber10.
• CommentAuthorEric
• CommentTimeDec 30th 2009
I second Mike's idea.
• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeDec 30th 2009
• (edited Dec 30th 2009)

As I said, I have the same opinion, too. And I also thought what Toby said: that we'll copy over to the nLab whatever material anyway. But if a separate web is what it takes for Andre Joyal to contribute, then I am willing to make that trade-off.

But I'll contact him again.

• CommentRowNumber12.
• CommentAuthorAndrew Stacey
• CommentTimeDec 30th 2009

If it is just a question of the statement on the homepage then I'm in agreement with Toby, Mike, and Eric. I'm especially wary of anything that creates the impression of "factions" within category theory. Whilst there are, of course, different points of view I would hope that we can accommodate these differences within the n-lab rather than having a different web for each. Of course, when it tends to be just one person that has these different points of view then we have personal webs, but when there is a sizeable body with each opinion then it's important to have both views presented in the same place (assuming, of course, that all the views are valid).

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeDec 30th 2009

Let's rephrase the HomePage and the nPOV such that it becomes clear that when we say "higher category theory" we mean "category theory and higher category theory", each being a reflection of the other.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeDec 30th 2009
• (edited Dec 30th 2009)

Okay, I rephrased the first paragraph at HomePage slightly, to address the above issues. Just a suggestion. Feel free to modify.

Also edited the slogan box at nPOV such that it links to both category theory and higher cat theory.

• CommentRowNumber15.
• CommentAuthorMike Shulman
• CommentTimeDec 30th 2009

Thanks! I guess the real question is whether the changes make Joyal any happier. If not, maybe we could invite him to take part in a discussion about how to phrase it better?

• CommentRowNumber16.
• CommentAuthorjoyal
• CommentTimeDec 30th 2009
First, I thank Urs for inviting me to join your discussion. I was surprised, and pleased, by your interest in my potential collaboration. I will have to learn some MathML before actually contributing. As you know, I have suggested creating a CatLab not subordinated to the nLab. Let me try to explain my position clearly. It is partly a question of image, but as you know, the image can be important, since it carries a message about the nature and the goal of an organisation. The nLab is already successful and it will probably inspire other peoples in other fields into creating something similar. Let us try to think about the future. Mathematics is divided into branches and there is a social aspect attached to the division. Most mathematicians feel at lost outside their field. Nothing can stop them from creating a Lab for working in their field if they want to. They will chose the name of their lab according to the name of their field and its steering committee will reflect the sociology of their field. But the division of mathematics into fields is somewhat artificial and it can be an obstacle to progress. Assuming that everybody will eventually have a Lab in their field, these labs should be connected. In other words there should be a network of interconnected labs. The payoff of such a network could be enormous in terms of expansion and better efficiency of research and education in mathematics. The name of the network should probably be generic (like MathLabs ?). The lab devoted to category theory could be called CatLab. Category theory and higher category theory could emerge as unifying disciplines by the number of connections to them.

In other words, I am inviting you to think about the future now.
Being a computer illiterate, I do not understand fully the nature and difficulty of the problem.
• CommentRowNumber17.
• CommentAuthorAndrew Stacey
• CommentTimeDec 30th 2009
• (edited Dec 30th 2009)

André, thanks for joining the discussion.

I would like to respond to the important part of what you wrote, but as it's late here and I need to think a little before I do, I shall hold off before doing so. However, I thought it worth clarifying the technical side - mainly to remove that from the discussion. There are no difficulties with what you suggest technically. The "nlab" is actually a family of "webs", which are interconnected as you picture. Thus the technology for what you envision is already in place.

Secondly, you don't need to know any MathML to contribute. The input syntax for the nLab is officially known as markdown+itex2mml. In practice, what that means is that you use basic LaTeX for mathematics and then there's a reasonably simple formatting syntax for the rest of the text (there's a "cheatsheet" when you edit a page). In fact, it's even simpler than that as there are a team of "lab elves" who go around cleaning up formatting and the like so you can just start editing and others will help with the formatting.

(Added in edit: the real host for the nlab is not ncatlab.org but mathforge.org. The name was chosen deliberately as an homage to sourceforge, the mainstay of open source projects.)

• CommentRowNumber18.
• CommentAuthorEric
• CommentTimeDec 31st 2009
• (edited Dec 31st 2009)
I suggest creating a new web called "CatLab" as requested. Can we give it a special domain that does not contain "n" in it?

http://www.mathforge.org/CatLab

?? That is, unless "catlab.org" is available, which I doubt :)

As Andrew pointed out, all such "webs" are pari passu and none is subordinate to another.

PS: Don't worry too much about formatting, itex2mml, etc too much. That is what the lab elves are for.
• CommentRowNumber19.
• CommentAuthorMike Shulman
• CommentTimeDec 31st 2009

Eric, I'd rather hang on a bit before creating a new web until I'm convinced that it's really necessary; first let me put forward my "plea for unity". (-:

To start with, André (welcome, by the way!) has quite a valid point that different communities of mathematicians will want to have different "labs" whose outlook and POV reflects the sociology of their field. In fact, that's always been my take on the nPOV: we aren't saying that our POV is the only valid one, just that it's ours, and other people with a different POV can start their own lab. And it would be all the better if these different labs could easily interlink to each other; the vision you present is quite an exciting one.

However, I'll be sad if the particular communities of "category theorists" and "higher category theorists" have POVs that are so irreconcilable as to require different labs. I like to think of myself as a member of both of these communities, and I don't look forward to having to think "where should this go?" when creating a new page, or remember "now which lab is that page on?" when creating a link to something like colimit or topos or 2-category. Do you really feel that category theory and higher category theory are so different as to need to be separated? Is it just the (somewhat exaggerated) rhetoric at the HomePage and nPOV and elsewhere on the nLab which is offputting to a non-higher category-theorist? If so, that can certainly be changed. I'd even be willing to consider changing the name of the nLab if necessary, although I'm not sure how other people would feel about that.

Given all the difficulties that category theory and higher category theory face in getting our ideas accepted by the rest of mathematics, I would much rather that we be united among ourselves. (-: Certainly we all have differences in viewpoint, but there are already noticable differences in viewpoint among the nLab contributors and we've managed to agree on common ground so far. Would you be willing to try joining the nLab community for a while first, and then if it really doesn't seem to be working out, we can fork the project then?

• CommentRowNumber20.
• CommentAuthorEric
• CommentTimeDec 31st 2009
• (edited Dec 31st 2009)
At the risk of both being redundant and of repeating myself

I second Mike's idea :)

I also considered suggesting changing the name of the nLab to be more inclusive, but I'm glad Mike said it out loud first :)
• CommentRowNumber21.
• CommentAuthorAndrew Stacey
• CommentTimeDec 31st 2009

I'm glad I held back as Mike's said pretty much what I thought too.

However, I think that it is worth remembering that the nLab is primarily a research tool for a particular group of people. As we say in the About page, that group is fairly loosely defined and we try to be very open to newcomers. That said, if someone wished to setup a similar project for a different research group then that would be a great idea and I would be willing to help with the setup and to look into ways to allow the projects to work together. But I agree with Mike in that I would be disappointed if that were necessary for "category theory" as opposed to "higher category theory".

With regard to the name, I don't think that it should be changed. The nlab "brand" is getting known and it would be a shame to lose all that hard work. Making the name more inclusive would also signal that the intention was to become more of a reference place than a research place - I would strongly argue against such a change.

That said, we can always point domain names to particular webs, or even particular parts of the nlab. We "own" ncatlab.org and mathforge.org and their subdomains. So we can have "http://catlab.mathforge.org" pointing to a different web, or even to category theory, if so desired. We could buy more domainnames, (but unfortunately catlab.org is taken), but 'mathforge' seems neutral enough that I don't see why that would be necessary at this stage.

The nLab is still in its infancy and it's worth thinking about how the project might grow and develop, particularly thinking about how people who don't particularly want to join our group might branch off on their own without the hassle of setting up a whole new project (and thus having to duplicate much of our work). But I'd like to think carefully about this before just trying it.

Here are some questions for André:

1. What do you see yourself doing on a lab, be it either the nlab or a spin-off?
2. Can you expand a little on why you are hesitant about doing that (whatever it is) on the nlab itself?
• CommentRowNumber22.
• CommentAuthorjoyal
• CommentTimeJan 1st 2010
Mike, I agree with everything you said, and with the nPOV of the nLab. Maybe I misunderstood the goal of the nLab.
I read that it is a group lab book for working in Physics, Mathematics and Philosophy. It has about 120 collaborators.
The nLab may be helpful to propagate the doctrine of (higher) category theory, but it is not its mission (at least officially).

I was among the category theorists of the 1970's who were convinced that category theory was soon going to conquer mathematics by unifying it. I can see in retrospect how naive we were. The strong momentum that the Grothendieck school had impulsed to category theory was still in full force and we had contributed to algebra, logic and topos theory. But things did not developed our way. Have you read the Princeton Companion to Mathematics edited by Timothy Gower and published recently? It was reviewed last November in the Notices of the AMS (the same issue of the Notices with the interview of Manin). One of my distinguished collegues justly observed that

>none of the reviewers were struck by the fact that in that survey Category Theory is one topic amongst 99 Mathematical >Concepts, with a single article (not well edited) and few other references. Equally none of the things which Manin >mentions (Feynman path integrals, higher categories, homotopy algebra) get a mention. It is reasonable to think
>that it never occured to the editors to highlight category theory as a way of thinking.

Many of my collegue mathematicians, some quite young, whom I respect highly for their competence in geometry, combinatorics or analysis, are proud of their ignorance of category theory.
They are dinausors, but dinausors were dominant on earth during more than 150 millions years!
I recall that in 1993 Paul Cohn told me that "category theory has all the characteristics of a sect".
I recall my shame when I would reveal to be a category theorist when presented to a high ranked mathematician.
I even tried to deny it for a while. Category theorists were the outcasts of the mathematical community

But the situation is changing now.
Thanks largely to the Russian school of mathematics.
Top mathematicians like Drinfield, Manin, Turaev, Kontsevich, Voevodski and Kapranov
have no inhibition in using category theory when useful.
Because of that, category theory has penetrated geometry and physics more deeply.
John Baez and the n-category caffe are playing an important role
in reshaping positively the image of category theory.

The unity and diversity of mathematics are complementary, not contradictory.
It would be very good for mathematics to have a neutral network of interconnected
labs reflecting this unity and diversity.
I think that category theory and higher category theory could prosper enormously in such a network.
Everyone should feel at home in his lab, without having to submit to a global ideology of
category theory, or of higher category theory, or of constructive mathematics, or anything else.
Most mathematicians are naturally opportunist, they amuse themselves with philosophy
and are suspicious of ideology.
They care about theorems, proofs, computations, ideas and tools.
I do not mean that philosophy has no value, but history shows
that it is not by itself an important driving force in mathematics.
Hardy the mathematician one said that "philosophy is good after dinner when smoking a pipe".
• CommentRowNumber23.
• CommentAuthorTodd_Trimble
• CommentTimeJan 1st 2010
This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>Dear Andr&eacute;</p> <p>I am very happy to see your support and interest in the nLab.</p> <p>You wrote:</p> <blockquote> Everyone should feel at home in his lab, without having to submit to a global ideology of category theory, or of higher category theory, or of constructive mathematics, or anything else. Most mathematicians are naturally opportunist, they amuse themselves with philosophy and are suspicious of ideology. They care about theorems, proofs, computations, ideas and tools. I do not mean that philosophy has no value, but history shows that it is not by itself an important driving force in mathematics. </blockquote> <p>I often wonder how ideological the nLab comes off to those looking in who are not directly involved.</p> <p>There is for example strong and explicit emphasis on constructive mathematics shot through the nLab. From my own perspective this is a good thing; if I begin writing a more classically-oriented article and someone (often Toby) comes through and gives it a good constructive going-over, I tend to learn a lot. To others though such things may read as exercises in "constructive correctness" (analogous to "political correctness" perhaps), making them either uneasy or intimidated or otherwise put off. Same with articles with implied "morals" (e.g. <a href="http://ncatlab.org/nlab/show/evil">evil</a>), no matter if they are written partly tongue-in-cheek.</p> <p>I don't think it's a case of anyone having to "submit" to an ideology (I just write however I feel, and others like Toby are free to add their POV), but I can see how others looking in might get a different impression. Perhaps we do need to be sensitive to a reputation of category theorists behaving with perceived missionary zeal (as I guess happened in the sixties and seventies) about the "right way" of thinking about things -- cf. Paul Cohen's remark.</p> </div>
• CommentRowNumber24.
• CommentAuthorEric
• CommentTimeJan 1st 2010
This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>Note: My opinion should be discounted because I'm merely an interested observer and can contribute little in terms of actual mathematical content.</p> <p>However...</p> <p>I think this vision the nLab regulars would like to see is nice in principle, but it seems clear to me that it is not going to happen. I suspect that Professor Joyal's views are shared by many (if not most) category theorists.</p> <p>When I see the statement</p> <blockquote> I think that category theory and higher category theory could prosper enormously in such a network. </blockquote> <p>I read this to mean that he believes (even after valiant attempts by nLab regulars) that category theory is distinct enough from higher category theory in both nature and audience to warrant separate places in this "network" we're beginning to envision.</p> <p>If I'm reading that correctly, then I think there could be no harm in creating a separate "CatLab" on this network and as Professor Joyal said</p> <blockquote> The lab devoted to category theory could be called CatLab. Category theory and higher category theory could emerge as unifying disciplines by the number of connections to them. </blockquote> <p>This is a beautiful, elegant, and simple idea. Instead of trying to force the connections, let them grow organically.</p> <p>It is utterly trivial to link from one web to another, e.g. CatLab to nLab and vice versa, so this argument about not being sure which "lab" to post to and the idea of copying all material from one lab to another seem like non-problems that are easily overcome.</p> <p>There already seems to be an established community, i.e. the CatTheory mailing list, dedicated to category theory and many of those are probably also interested in higher category, but certainly not all of them. My suggestion is to try to build CatLab around this existing community, similar to the way nLab was built around the nCafe, so that those on the CatTheory mailing list have a place to point to for definitions etc and let the links between the two "webs" (and hopefully more in the future) evolve naturally.</p> </div>
• CommentRowNumber25.
• CommentAuthorzskoda
• CommentTimeJan 1st 2010

I do not know any MathML and do not intend to learn it as it is not an issue in nlab: we write in a sourcecode which is resembling LaTeX plus double brackets and other tricks to put interlab, intralab and external links.

It is indeed interesting as Profs. Joyal and Cartier (the latter in an article on the concepts of a space) that the new wide wave for the category theory has been in part prompted by non-categorists Russian school, rather than the French school of algebraic geometry, if we subtract the phenomenon of Simpson's school. This is an interesting topics to discuss (and possibly learn something from). It is not that category theory was ever wide popular in Moscow, certainly less than in France. Algebraic topology school was mainly centered around examples and calculational problems and some deep conjectures, mainly those of Novikov. Russian algebraic geometry school however a possible advantage of, as Albert Schwarz, pointed to me, by being less separated from theoretical physics, and most of the main Russian "revolutionaries" of geometry/topology/algebra including Drinfeld, Novikov, Feigin, Manin, Kontsevich looked at it extensively, and the role of mathematical physicists is not negligeble in mathematics (Fadeev, Knizhnik, Polyakov, Schwarz...). Mathematical physics is a strong community in France, but more interacting with combinatorics and analysis community rather than with modern geometers. Another factor is the profecy of Beilinson which stems from deep applications while it is formulated and studying using very modern and categorical techniques. Manin was on the other hand, more important in a role of modern educator and mentor, being aware of Grothendieck's doctrine and being (apart from Arnold) the most popular professor of MGU in its golden period of 1970s and 1980s. This brought a new generation including Kapranov, Bondal, Orlov, Tsygan, Tamarkin, Kontsevich, Goncharov, Voevodsky. Hinich, Schechtman, Soibelman, E. Frenkel, Kaledin and others, who do not have the burden into completing standard but unfinished works of Grothendieck school in algebraic geometry but do new mathematics with all the Grothendieck's work and standard mathematical physics as a school background.

In representation theory the influence of Beilinson-Bernstein-Kazhdan, who are highly educated in categorical methods and modernized homological algebra, continued after their transfer to the west (and continued by their pupils Finkelberg, Bezrukavnikov, Gaitsgory, Arinkin etc. and other embracers of the new categorical points of view in representation theory like Milicic, Mirkovic, Vilonen, Schmid, Rouquier to name a few). Gel'fand himself was good in fostering and praising deep insights which could involve such categorical methods but himself was definitely not inclined nor used to use much of say adjoint functors formulations in his business. Japanese school in representation theory is here quite modern and I am afraid still underappreciated.

In the same time American school has been more modern in homotopy theory than the Russian school (unfortunately, Novikov left algebraic topology in his best period around 1980 and started doing mathematical physics). Though for an average mathematician in US, as I can witness from the years of my study in late 1990s, the low-dimensional manifolds, especially 4-dim topology and the interaction with string theory was much more popular than the heart of homotopy theory. This was also about the world trend in 1980s and 1990s, highly supported by influence of Sir M. Atiyah. Rather intuitive and direct methods of manifold gluing, characteristic classes, classical gauge theories, and then the Gromov-Floer symplectic geometry revolution did not need much of deep category theory at its start, though Fukaya and Kontsevich benefited from introducing the higher categories exactly into that business and the categorification in representation theory is now intertwined with manifold geometry (Khovanov homology etc.).

• CommentRowNumber26.
• CommentAuthorzskoda
• CommentTimeJan 1st 2010

Prof. Joyal wrote: I read that it is a group lab book for working in Physics, Mathematics and Philosophy. It has about 120 collaborators. The nLab may be helpful to propagate the doctrine of (higher) category theory, but it is not its mission (at least officially).

I think the 120 is exaggarated, most of these were involved so ar in few entries; only about a ten people contributed extensively so far. My understanding is that the nLab's mission is convenient setting to put notes and use it for whatever constructive reason in mathematics. It is not necessarily exposition or necessarily research or if research a new research. Every instance of this "work" may be a basis but does not have to be of new developments in the lab or out of the lab. It is simply making your notebooks part of the wider effort. I can not imagine how would a work with its emphasis in category theory NOT propagate category theory (except if we are even collectively immature in the understanding of the subject). It is a mixture between a research project and a wikipedia like online information source, but without the limitations of wikipedia ("publish only undisputed, generally accepted, published and checked information", "no original research" and "sign those permanent licences"; instead we remember the authorship, put original stuff, put tentative stuff, and try controversial points of view).

• CommentRowNumber27.
• CommentAuthorTobyBartels
• CommentTimeJan 1st 2010

For counting collaborators: The list at http://ncatlab.org/nlab/show/Contributors includes everyone who made a substantive edit and gave some identification. This includes several who contributed only to Online Resources and so could perhaps be removed. The list at http://ncatlab.org/nlab/authors includes everyone who signed a name along with how many pages they've edited; it includes a few spammers but also gives a good idea of who is a major contributor. The list at http://ncatlab.org/nlab/list/people includes those contributors who have created a page about themselves but also quite a few mathematicians who have never contributed, in a few cases because they are long dead; it may help identify the most dedicated contributors but provides a very poor count.

• CommentRowNumber28.
• CommentAuthorAndrew Stacey
• CommentTimeJan 1st 2010

I think that there are a couple of issues that are at risk of getting compounded so I would like to list them to separate them out. They are:

1. How can we persuade Prof. Joyal to join the nLab?
2. In what ways could the nLab expand?

Eric's most recent comment triggered a train of thought for me that may be worth sharing. The different labs are centred on certain people or groups of people (not disjoint) and it is that which really determines where content is put, not the specific content itself. From reading the descriptions of the personal webs, this seems true: people put stuff on their personal web when they feel that they are acting alone and put stuff on the nLab when they feel that they are acting as part of the main group.

So I think that a separate lab needs a separate group of people, rather than a separate topic. Eric's suggestion of a lab for the category theory mailing list seems like a good one to me - there have been quite a few small results that have been worked through on the list which it would be great to have written somewhere a little more accessibly than in the archives of that list, but I can see that many on the category mailing list would be hesitant at adding to the nLab itself; but being able to link between the two would be very useful. Of course, this would have to be put before the steering committee here and suggested to the list. (This could also be done for the algtop list, I guess.)

On other things, André said:

Everyone should feel at home in his lab, without having to submit to a global ideology of category theory, or of higher category theory, or of constructive mathematics, or anything else.

I'm a differential topologist. I get vertigo in 2-categories. I still feel unsure in basic categories! But I feel "at home" in the nLab. The nPOV doesn't get imposed on me, rather when I add something then someone comes along and adds the nPOV. My point of view doesn't get removed, just added to. And, as Todd said, I learn something.

But I still don't have a sense as to how you, André, would like to use the nLab, or something like it. Without that then I feel that I can't really do more than suggest vague ideas. From my point of view, it would be great having you involved because I could learn a lot. But I'm not sure what's in it (or potentially in it) for you. As I've said elsewhere, the nLab is ultimately selfish - we use it because we think it helps with our day jobs! How do you think that the nLab could help you?

• CommentRowNumber29.
• CommentAuthorzskoda
• CommentTimeJan 1st 2010

none of the reviewers were struck by the fact that in that survey Category Theory is one topic amongst 99 Mathematical Concepts, with a single article (not well edited) and few other references.

It is symptimatic, though that as many as 3 reviewers did complain about not enough cohomology, the subject which is naturally placed only within homotopical algebra and higher category theory:

Birch: I note that cohomology gets short shrift; it is a valuable and pervasive technique, but may be hard to write about attractively.

Donaldson: I was hoping to find a broad discussion of the influence of cohomology in various guises (surely one of the main developments of the twentieth century), but was disappointed. It would have been interesting and topical to see more on quantum field theory, as a notable idea “that mathematicians are grappling with at the beginning of the twenty-first century” (although there is some coverage of this under the headings “Mirror symmetry” and “Vertex operator algebras”).

Macintyre: For an idea so pervasive in modern mathematics, cohomology gets rather little coverage, except for three pages in Totaro’s beautiful paper. One can hope for much more in a revised edition.

• CommentRowNumber30.
• CommentAuthorMike Shulman
• CommentTimeJan 1st 2010

I am total agreement with Andrew.

• CommentRowNumber31.
• CommentAuthorjoyal
• CommentTimeJan 1st 2010
Many thanks to Andrew, Eric, Mike, Toby, Todd, Urs and Zoran for their very thoughtful comments. I do not want to respond before I obtain a better knowledge of the nLab. This could take me a couple of weeks. Also, I would like to know if some of my collegues in Montreal are interested in working in a Lab devoted to their field (combinatorics, geometry and topology). I also want to put a few papers on the arXive early this month. Unlike my wife, I find it difficult to do two things at the same time. I hope we can continue our conversation soon. Best wishes for the new year, andré.
• CommentRowNumber32.
• CommentAuthorzskoda
• CommentTimeJan 3rd 2010
• (edited Jan 3rd 2010)

Topology in its modern focus (homotopy, cohomology, sheaf theory) is one of the central topic of nLab, and a partial list of entries can be found at topology (nlab). Combinatorics is not significantly present so far. Geometry is somewhere in between, I am trying to push writing articles related to algebraic geometry, Urs is trying to put much differential geometry and Lie theory...especially synthetic approach.

• CommentRowNumber33.
• CommentAuthorJohn Baez
• CommentTimeJan 3rd 2010
I don't think the nLab crew should be in any hurry to create new "Labs". To prosper, any such thing needs a few people who like to write a lot. When this happens, I think we'll know it. The nLab arose because Urs was desperate to write lots of stuff. So I'm not sure it makes sense to create a CatLab, for example, and then see if anyone writes anything there.

"Nobody should start to undertake a large project. You start with a small trivial project, and you should never expect it to get large. If you do, you'll just overdesign and generally think it is more important than it likely is at that stage. Or worse, you might be scared away by the sheer size of the work you envision. So start small, and think about the details. Don't think about some big picture and fancy design. If it doesn't solve some fairly immediate need, it's almost certainly over-designed. And don't expect people to jump in and help you. That's not how these things work. You need to get something half-way useful first, and then others will say "hey, that almost works for me", and they'll get involved in the project."
• CommentRowNumber34.
• CommentAuthorMike Shulman
• CommentTimeJan 4th 2010

Good point.

• CommentRowNumber35.
• CommentAuthorAndrew Stacey
• CommentTimeJan 4th 2010

I agree with John's point and that's why I suggested that a possibility would be a 'catlab' for the category theory mailing list. I would present it to them as a "sketch pad" where they could write things with a little more structure than is possible by email. For example, the recent discussion on the "snake lemma" contained several diagrams that kept getting mangled by email readers. The authors could have put them on a wiki page (and kindly lab elves could have cleaned them up a little) and then people could just have said "see X for a better rendition of the diagram".

I think that this does fit in with Linus' advice: it's a small thing - an add-on to the mailing list - and there's a definite group of people - the readers of that list - who would benefit immediately. We would gain by providing this service because it would be easy for the authors to link to stuff in the nLab itself via the Wikilinks and, sometimes, people would follow those links and decide to improve articles in the nLab itself.

Because the nLab itself was first, it is and always will be unique. We should think a little about how new labs might grow. I agree that setting up "catlab" with the intention of it being "for the greater good of category theory" is daft, but I think that the above idea of an aid to the category theory mailing list is plausible and may be a reasonable model of how new labs will grow organically out of the main nLab.

• CommentRowNumber36.
• CommentAuthorUrs
• CommentTimeJan 4th 2010

i agree with John and Andrew above. In fact, i see very general agreement here among all nLab regulars.

Andre has a good point that in the future, at some point, it will be great to see lots and lots of math on the web, in a massive amount that expands beyond the scope of the nLab, but I think John is quite right that it's not right now the time to start such a branching.

Neverthess , and I gather from Eric and Andrew that we are converging on this and agreeing on this, too, I would really like to satisfy Andre's request and create a web for him. Please, Andrew or Toby, let's create this web! Let's give it a title that goes in the direction of "catLab", maybe some slight variant. I can't stand the thought that we keep discussing the pros and cons of an extra web, while Andre Joyal is waiting for us, eager to add material to such a new web.

Once it's in existence, we'll see what happens with it. I don't expect that it will immediately explode in size, so that in a few months we may come back, have a look at it and come back to the discussion here, then all with a better picture, deciding on how to proceed with the new web.

• CommentRowNumber37.
• CommentAuthorEric
• CommentTimeJan 4th 2010

My vote is "CatLab" (Urs is terrible with capitalization!) :)

That is what Professor Joyal suggested and there is no good reason to go with anything other than what he suggested.

One important aspect that is emerging is that these "labs" need to evolve around existing communities, e.g. nCafe -> nLab, so I think it is important to stress that "CatLab" is dedicated to the Cat-Theory mailing list community. A place where they can collect thoughts and place notes. I'm sure there is an extreme wealth of knowledge buried on that mailing list (I didn't even realize it existed and was so active) and CatLab can be a store for some of that knowledge.

And... I'm a little surprised that Urs passed up the opportunity to say that CatLab does not need to be one more thing on the to-do list. It is a tool for completing your to-do list :)

• CommentRowNumber38.
• CommentAuthorAndrew Stacey
• CommentTimeJan 4th 2010

Nevertheless, and I gather from Eric and Andrew that we are converging on this and agreeing on this, too, I would really like to satisfy Andre's request and create a web for him. Please, Andrew or Toby, let's create this web! Let's give it a title that goes in the direction of "catLab", maybe some slight variant. I can't stand the thought that we keep discussing the pros and cons of an extra web, while Andre Joyal is waiting for us, eager to add material to such a new web.

I understand your eagerness to get André involved! But I'm still not sure everything's quite settled yet. Eric and I have floated the idea of a web for the category theory mailing list, rather than particularly for André. I certainly have no objection to André having his own personal web (and I'd be surprised if anyone else did either, but I'm only speaking for myself) but I'm not clear that that is what he wants. From the initial discussion, it seemed that he wanted a web "for category theory". This met with some resistance, of various kinds, and Eric's proposal seems (to me) the closest workable idea to the original proposal. But this idea has yet to receive any comment from André himself as to whether or not it fits his ideas.

Of course, Eric's idea doesn't need André's approval: as the intention is for it to be for the mailing list, it is for them as a whole to decide not André alone. But as the idea came from the original discussion with him, I'd certainly want to know what he felt about it before going further.

From André's last comment, I don't think that he is poised over the keyboards waiting to unleash a torrent of mathematics on the lab. So we should take the time that he has granted us in that comment to figure out (hopefully with input from André) what the best response is.

In summary, I see three possibilities:

1. A personal web for Andr´, say "andrejoyal",
2. A new not-quite-personal web for the category mailing list, say "catlab", possibly with its own subdomain so it's not so tied to the higher category theory (this won't affect any of the ability to link between webs),
3. A web for "category theory".

Of course, these are not mutually independent. I have no problem with either 1 or 2; option 3 has been fairly well discussed and I'm against it. The only reason that I am hesitating about implementing 1 or 2 is that I don't know that the people for whom they are intended will use them. So, questions for André:

1. Do you want a "personal web"?
2. Do you think a "web" for the category mailing list would be useful? (And would you help us promote it?)

As an example for (2), you (André) recently suggested to me (via the list) some ideas on how to look at lambda-rings. I've yet to fully understand what you were saying - partly due to it being exams and Christmas, but also because I find it hard to read ascii mathematics and feel that to really understand it, I should write it out on paper (shock, horror!) or on a wiki page. If you had started out that way, the whole process would have been much quicker.

• CommentRowNumber39.
• CommentAuthorAndrew Stacey
• CommentTimeJan 4th 2010

Whoops! Cross-posted with Eric there.

My hesitation with setting up 'catlab' for the category theory mailing list is purely that no-one's yet asked them if any of them think it would be a good idea. I'd rather at least set out a proposal for them before actually doing it - I think it's more polite that way.

• CommentRowNumber40.
• CommentAuthorTobyBartels
• CommentTimeJan 4th 2010

I thought that we were waiting for André to return a couple of weeks after posting #31 (which he posted a couple of days ago). So I basically agree with everything that Andrew wrote in #38.

• CommentRowNumber41.
• CommentAuthorUrs
• CommentTimeJan 4th 2010
This comment is invalid XHTML+MathML+SVG; displaying source. <div> <p>Okay, never mind me. It seems that I agree, too, with everything you all say, except that I feel creating a web of the kind requested, even if not what we envision, would serve a good Sandbox-type purpose and open the opportunity to see in practice what it would actually be used for, not precluding the possibility that we all decide later that the content that appears there be moved elsewhere in the end.</p> <p>But never mind me. I remember similar frictions earlier with the nLab itself. With these matters of public interaction I always think that theoretizing never leads much anywhere, while testing out how things develop in practice is everything.</p> <blockquote> From André's last comment, I don't think that he is poised over the keyboards waiting to unleash a torrent of mathematics on the lab. </blockquote> <p>Sure, but that's without the web being available. Would you all have <em>planned</em> to add to the nLab the stuff you added now that it exists? Even though you often may have "better" things to do?</p> <p>But, as I said, never mind.</p> </div>
• CommentRowNumber42.
• CommentAuthorMike Shulman
• CommentTimeJan 4th 2010

I also agree with Andrew.

• CommentRowNumber43.
• CommentAuthorzskoda
• CommentTimeJan 4th 2010
• (edited Jan 4th 2010)

I do not understand what does it mean a "lab for category list" ? I know what is category list and receive it, but do not understand what kind of lab purpose should be named by another INSTANCE of multimedia. That is like creating a radio program called "FOX TV".

I mean I can not assume that you meant to create an another lab with restricted access (only personal labs should be such in my opinion), so declaring a lab for category list instead of Catlist is just a title. I propose to talk content instead.

• CommentRowNumber44.
• CommentAuthorUrs
• CommentTimeJan 4th 2010

I think the idea was that the CatTheory mailing list participants might want a wiki in parallel to their mailing list, where they would be able to work out the stable ideas that are being discussed on the list.

Sort of the original idea of how the nLab was supposed to be used by the participants of the n-Catgeory Cafe blog. (Only that these participants haven't quite appreciated that idea.)

• CommentRowNumber45.
• CommentAuthorEric
• CommentTimeJan 5th 2010

If we create a CatLab web and no one comes, is it a big deal?

I know Urs is on the Cat-Theory mailing list and he at least would contribute something to the CatLab. Probably Toby and John too and now that I know it exists and is so active, I will probably transfer content as well.

I don't think we need "CatLab" AND "category theory" though. Come on guys! :)

• CommentRowNumber46.
• CommentAuthorTobyBartels
• CommentTimeJan 5th 2010

I don't think that my presence on CatLab is terribly important, so I didn't mention this before, but since Eric did:

Unless a CatLab takes off on the strength of other contributors (and possibly not even then, unless everybody switches away from the nLab), I almost certainly will not contribute to the CatLab myself. I already have a Lab.

Of course, if Eric copies all of my stuff from one Lab to the other, there's nothing wrong with that.

• CommentRowNumber47.
• CommentAuthorAndrew Stacey
• CommentTimeJan 5th 2010

If we create a CatLab web and no one comes, is it a big deal?

Yes, I think it is. And that's why I'd want to ask them first if they like the idea. At the very least, it diverts our resources from the nLab proper. It would only work if there was a sizeable number who didn't want to contribute to the nLab but did want to have somewhere to scribble things down. That's quite tricky to judge, which is why I'd like André's opinion on it as he was (is?) hesitant to contribute to the nLab itself but seems interested in the general idea.

• CommentRowNumber48.
• CommentAuthorUrs
• CommentTimeJan 5th 2010
This comment is invalid XHTML+MathML+SVG; displaying source. <div> <blockquote> And that's why I'd want to ask them first if they like the idea. </blockquote> <p>I am sceptical that this would lead very far. The average participant there probably has at most a very vague idea of what the question is actually about. Moreover, my impression is that sociological aspects play a big role on the CatTheory mailing list, in that participants are more likely to follow the lead of an important name.</p> <p>Therefore what I can imagine would work is that we equip Andre Joyal with a web, and then he might announce on the CatTheory mailing list that he will start adding material to that. Better yet, he might add some material and then point the CatTheory mailing list to the existing material, so that they can see what exactly it is that is being proposed to them.</p> <p>I keep in mind the way the nLab was born. Before it existed we had endless discussion on the blog about the advantages or not of creating a wiki in parallel to the blog. People had many opinions, but nobody had an idea what exactly this opinion was about. Nobody knew what the nLab would be like until it started to exist. With the thing in existence as a real tangible thing, it then became possible to try to steer it in certain directions.</p> <p>I expect this is what it will take for new webs, too. Somebody who creates facts by starting something. And then seeing if others join in. For what it's worth, that seems to be also one aspect of the Linus Torvald quote from above.</p> </div>
• CommentRowNumber49.
• CommentAuthorEric
• CommentTimeJan 5th 2010
• (edited Jan 5th 2010)

Most current webs have very little if any activity. These don't seem to have caused much damage. I still don't see the harm in just creating CatLab and seeing what happens. We are WAY over thinking this (see Linus).

Wiki Webs:

*
Alex Hoffnung (published version)
1 page by 1 author - Last Update: May 13, 2009 16:38:21
*
BWebster
9 pages by 3 authors - Last Update: November 15, 2009 22:34:14
Last Document: desiderata for KI-HRT Revised by Ben Webster (74.104.47.39)
*
Bruce Bartlett
3 pages by 3 authors - Last Update: October 28, 2009 18:24:04
Last Document: Geometric quantization and the path integral in Chern-Simons theory Created by Bruce Bartlett? (146.232.65.7)
*
Chris Rogers
4 pages by 2 authors - Last Update: November 16, 2009 06:18:14
Last Document: graded supermanifolds and Courant algebroids Revised by Chris Rogers? (138.23.233.3)
*
DStevenson
1 page by 3 authors - Last Update: October 31, 2009 00:12:13
*
David Corfield
26 pages by 4 authors - Last Update: November 27, 2009 17:03:53
Last Document: The Principles of Art Revised by David Corfield (81.154.250.179)
*
David Roberts
28 pages by 6 authors - Last Update: October 1, 2009 12:13:13
Last Document: local epimorphism Created by David Roberts (203.171.199.209)
*
Domenico Fiorenza
4 pages by 4 authors - Last Update: January 5, 2010 09:34:51
Last Document: over quasi-category Revised by domenico_fiorenza? (80.181.56.236)
*
Doriath
14 pages by 9 authors - Last Update: November 24, 2009 00:33:01
Last Document: Zen Garden CSS Sandbox Created by Daniel Schäppi? (128.135.194.243)
*
Eric Forgy
55 pages by 9 authors - Last Update: January 4, 2010 15:23:35
Last Document: Noncommutative Stochastic Calculus Created by Eric Forgy (119.247.164.4)
*
James Dolan (published version)
2 pages by 3 authors - Last Update: June 8, 2009 19:59:49
Last Document: Algebraic Geometry Revised by John Baez? (99.11.157.15)
*
John Baez
5 pages by 5 authors - Last Update: December 17, 2009 14:03:37
Last Document: Towards Higher Categories Revised by Urs Schreiber? (193.198.162.13)
*
Michael Shulman
53 pages by 7 authors - Last Update: December 23, 2009 06:36:12
Last Document: size structure Created by Mike Shulman (67.189.60.12)
*
Schreiber
103 pages by 11 authors - Last Update: November 20, 2009 22:36:03
Last Document: Seminar on (?,1)-Categories and ?-Stacks Revised by Toby Bartels (173.60.119.197)
*
Schreiber private
33 pages by 4 authors - Last Update: December 1, 2009 18:51:34
Last Document: Kan dendroidal sets Revised by Urs Schreiber (84.246.5.106)
*
Tim Porter
6 pages by 4 authors - Last Update: July 12, 2009 13:13:07
Last Document: topological data analysis Revised by Tim Porter (84.71.90.75)
*
Toby Bartels
5 pages by 2 authors - Last Update: November 9, 2009 18:27:23
Last Document: Sandbox Revised by Toby Bartels (71.103.255.108)
*
Todd Trimble (published version)
5 pages by 3 authors - Last Update: September 9, 2009 20:44:06
Last Document: Epistemologies Revised by Todd Trimble (69.118.56.215)
*
Zoran Skoda
45 pages by 4 authors - Last Update: December 31, 2009 02:21:15
Last Document: hom09 zadaci Created by Zoran Škoda (93.138.2.48)
*
nLab
2712 pages by 172 authors - Last Update: January 4, 2010 18:28:35
Last Document: tangent (infinity,1)-category Created by Urs Schreiber (88.128.82.168)
*
nLab meta
9 pages by 9 authors - Last Update: December 31, 2009 15:08:58
Last Document: n Forum FAQ Revised by Toby Bartels? (71.31.221.223)

• CommentRowNumber50.
• CommentAuthorjoyal
• CommentTimeJan 17th 2010
Tony Bartel wrote on the CatLab page

[We are fast reaching the point (if we are not already there) that this working example no longer fits on one page, so if you want to keep going, André, then you should probable return to the discussion on the Forum and suggest that the steering committee create a CatLab web now.]

On the same page, I wrote

[I warmly thank the nLab community for their generous response to my suggestion. I am presently very short of time, but I will try to spend some learning the wiki-art during the next few weeks. The CatLab is an offspring of the nLab, not yet fully shaped and not yet born. Like every child, he has no shame in feeding to the breast of his mother. It will probably cannibalise the nLab a lot! I will do a lot of cutting and pasting, this is how I can learn quickly.]

The first thing I would like to do is to give an exposition of basic category theory using the natural model structure on Cat together with other homotopical ideas to explain many aspects of the theory. I feel that this
is important for future research in the field. But I am not sure the CatLab is the right place for that.
Maybe I should write some kind of wiki-book, a CatBook? In any case, if you agree to create a CatLab web now, I would like to spend some time, maybe a month, to give it an initial shape before going public.
• CommentRowNumber51.
• CommentAuthorUrs
• CommentTimeJan 18th 2010

if you agree to create a CatLab web now, I would like to spend some time

I am definitely in favor of this and hope we can find a quick agreement on it within the steering committee.

While this is in the process, you could, if you don't feel like losing more time on it, probably start writing this or that in entries newly created on the nLab. If there is really the need, we can still copy them over to the CatLab later.

• CommentRowNumber52.
• CommentAuthorjoyal
• CommentTimeJan 18th 2010
Dear Urs,

I thought a bit about the nLab and what the creation of other labs could represent.
I would like to share my thoughts with you and know what you think.
I find it difficult to describe abstractly what the nLab is.
but this description is not precise enough.
It is a lab book, but the book could not exists without a community around it.
It is an offspring of the n-café, but what is the n-café?
Surely, the nLab is all this.
The nLab is unique in its kind, but deciding what it is may decide what it will be.
Let me suggest a direction for thinking about it.
It as a living organism.

Life is the greatest splendor of the universe, not the planets, not the stars, not the galaxies.
We may not know what we are, why we are here, but we know we want to live.
We are animals, but of a different kind. Let me stress some of the differences.
The first is probably the dexterity of our hands.
They can be used for an infinite number of things, from trowing a stone
to playing a piano, or for the caress of love.
The second difference is probably the virtuosity of our vocal system.
We can scream, sing and talk.
Our voice can communicate virtually an infinite number of emotions and ideas.
An omnious difference is the capacity of our brain.
We can have new ideas and understand others.
We can remember the past and make plan for the future.
Another important difference is our social organisation.
We are depending enormously on each other for survival.
Unlike most animals, we are physically and individually weak.
All human babies are premature.
It can takes a few decades for a youngster to become independant from his parents.
We are all depending on a social organisation.
It is wrong to think that we should be independant from each other and compete all the time.
Collaboration is probably more important than competition to explain the success of the humain species.
Competition is important too, but there should be a good balance between the two.
Well, I apologise for bringing ideas that you all know very well.
But if I bring them, it is because I think they are presently very important for our survival.
If we do not question the present culture and wake up to new alternatives,
I think very sadly that our civilisation will not survive climate warming.
Humanity itself may not survive the destruction of the biosphere.
Sciences and techniques will help for fighting the problem of climate warming,
but I do not believe that the problem can be solved by sciences and techniques alone.
There are strong conservative forces, the dark forces (not the evil forces), for doing nothing.
They are rooted in ignorance, vested interest, greed, blindness, crazyness, etc.
There are dark forces in each one of us.
The dark forces will do everything to preserve the statu quo, and if they succeed, we all fail.
We have an obligation to beat them.
But for this, peoples will have to unite and be very creative.
This is why we need some kind of cultural revolution, or cultural metamorphosis.
I am trying to avoid using the word revolution because of bad examples from the past.
I have only a vague intuition of what this metamorphosis could be.
I guess it is up to everyone to invent it, to discover it.
But we should all make a serious effort to think about it.
The anxiety created by the perspective of a future apocalypse can be tempered
by an increasing solidarity between the peoples, by new forms of action,
and new forms of organisation.
But we should not wait, time is running out.
It is now or never.

So, what is the connection with the nLab?
I do not know exactly!
But if really the nLab is a living organism, it should reproduce itself!
I do not mean that it should duplicate itself, make a copy of itself.
It could replicate by permitting changes in its genes, in its structure.
Some descendants will be successful and others will die.
But new unexpected forms could develop, and possibly a kind of ecosystem.
If we succeed in imitating life, we will be on the winning side.

I do not think that these ideas are absolutely crazy.
Other ideas will be needed to succeed.
There will be a lot of obstacles and a lot of practical problems to solve.
I am anxious to know what you think.

Yours truly,
André
• CommentRowNumber53.
• CommentAuthorUrs
• CommentTimeJan 18th 2010
• (edited Jan 18th 2010)

Dear André,

it is a pleasure to be subjected to your thoughts. Be it in your articles, your lectures or be it your private philosophical thoughts. I think we all feel honored to have you around here.

But if really the nLab is a living organism, it should reproduce itself!

Okay, possibly! Let's see what happens: the LabElves are pleased to present your Cat Lab now:

For the moment we called it "Joyal's CatLab" instead of just "CatLab", since you indicated that you would first work on it a bit just for yourselves. Later on, the name can easily be changed.

Please don't hesitate to get back to us with whatever questions about the technicalities or other requests for technical help you might have!

Looking forward to it,

Urs

• CommentRowNumber54.
• CommentAuthorUrs
• CommentTimeOct 5th 2021
• (edited Oct 5th 2021)

10 years later… (9 years after that project had died out…)

$\,$

Part of the above discussion somehow ended up on an nLab page here.

Since it makes no good sense to keep it there, I am hereby deleting that page and moving its content to here, just for the record:

begin forward of old discussion

# Contents

## Idea

A very interesting discussion took place at the nForum involving André Joyal, Urs Schreiber, and others:

It was there that the germ of a potentially exciting idea arose. Just as the nLab itself arose out of the needs of a community built up around the nCafe, could a new CatLab be built around the Category Theory Mailing List?

The CatLab would be pari passu with the nLab and serve as a model for other mathematics communities.

Here is the specific invitation extended by André:

First, I thank Urs for inviting me to join your discussion. I was surprised, and pleased, by your interest in my potential collaboration. I will have to learn some MathML before actually contributing. As you know, I have suggested creating a CatLab not subordinated to the nLab. Let me try to explain my position clearly. It is partly a question of image, but as you know, the image can be important, since it carries a message about the nature and the goal of an organisation. The nLab is already successful and it will probably inspire other peoples in other fields into creating something similar. Let us try to think about the future. Mathematics is divided into branches and there is a social aspect attached to the division. Most mathematicians feel at lost outside their field. Nothing can stop them from creating a Lab for working in their field if they want to. They will chose the name of their lab according to the name of their field and its steering committee will reflect the sociology of their field. But the division of mathematics into fields is somewhat artificial and it can be an obstacle to progress. Assuming that everybody will eventually have a Lab in their field, these labs should be connected. In other words there should be a network of interconnected labs. The payoff of such a network could be enormous in terms of expansion and better efficiency of research and education in mathematics. The name of the network should probably be generic (like MathLabs ?). The lab devoted to category theory could be called CatLab. Category theory and higher category theory could emerge as unifying disciplines by the number of connections to them.

In other words, I am inviting you to think about the future now.

After being reassured that there was no need to learn MathML (CatLab would be based on itex, a close cousin to LaTeX), he continued:

The unity and diversity of mathematics are complementary, not contradictory. It would be very good for mathematics to have a neutral network of interconnected labs reflecting this unity and diversity.

I think that category theory and higher category theory could prosper enormously in such a network. Everyone should feel at home in his lab, without having to submit to a global ideology of category theory, or of higher category theory, or of constructive mathematics, or anything else.

Before rushing into the creation of CatLab, it was the purpose of this page to serve as a seed for its creation. The virtual ribbon cutting should be orchestrated by an active member of the Category Theory Mailing List and this page may serve as something of a CatLab sandbox to help potential contributors get familiar with the possibilities.

+– {: .standout} A nascent CatLab may now be found at joyalscatlab, although it's final shape has yet be determined. =–

## Discussion

André: I warmly thank the $n$Lab community for their generous response to my suggestion. I am presently very short of time, but I will try to spend some learning the wiki-art during the next few weeks. The CatLab is an offspring of the nLab, not yet fully shaped and not yet born. Like every child, he has no shame in feeding to the breast of his mother. It will probably cannibalise the nLab a lot! I will do a lot of cutting and pasting, this is how I can learn quickly. I hope I will not mess things up! I apologise for the temporary disorganitation (posted by AJ).

Eric: No worries and no rush. It’s great to see how this material springing here and I’m sure CatLab will be ready for launch very soon. If you have questions, feel free to ask them either here or the forum. Since we’re getting the hang of the wiki, my suggestion is to ask technical questions here. The answers will likely end up being added to HowTo and the FAQ. Cheers!

## Further developments

André: I have interrupted working in the CatLab last Spring because of some urgent things to do. I hope to return in some near future. There was recently a discussion in the category list about terminology used in the nLab (the “evil” terminology). The discussion drifted and John mentioned his implication into fighting the ecological disaster. I applaud to John’s involvement, but I believe his position is overly pessimistic. But my reply to John was blocked by the moderator of the category list for technical reasons that I do not understand. I am reproducing this reply here:

October 1,2010

Dear John,

I thank you for your answer. The arguments of Saul Griffith according to which the planet is heading toward an ecological disaster are overwhelming. But he does not conclude (as you seem) that disaster is inevitable and the situation hopeless. He said that the problem can be solved with something like a global war effort. Pessimism is very dangerous because it is self-defeating. Beating the Nazi seemed impossible to many peoples in 1940. A climate expert like James Hansen is refusing to succomb to pessimism.

Let me express my opinion on some aspects of the problem of climate change. You should take it as the opinion of a collegue, or of a citizen, not of an expert. As you know very well, there is presently a large consensus in the scientific community about the gravity of the problem. So why are the politicians not acting? I guess this is because our democratic systems are defective. We all know that politicians are serving two masters: their electors and large corporations. They know where the money is. Public opinion is been manipulated by publicity and propaganda. We are brainwashed to think that we live in the best of all possible worlds, to think that nothing could fundamentally change except for the worst, to think that we all live to maximize our personnal pleasure, to think that all act of generosity is motivated by egoism, to think that the deep mystery of life and of the world can be captured by a few slogans. The problems of democracy have been analysed in more books than I can read. Our elected representatives are seldom acting for us.

Demo-cracy = power of the peoples

Clearly, something does not work. Democracy is presently failing to empower peoples collectively. Citizens are depressed and angry. I think we may try to cure ourselves from this collective depression by realising a collective project. It does not have to be a project on ecology or climate change, only something that we may do very well. It could be a project in our own backyard, mathematics! I believe our field needs to be renovated, reformed or, if you prefer, revolutionised. There are too many barriers, intellectual and professionnal, between the different fields of mathematics, including between pure and applied. Mathematicians from different fields can hardly understand each other, with the exception of a few mathematicians mastering more than one fields. Many of these barriers are somewhat artificials. Of course, like language barriers, they can be very real. It is natural to specialise, as it is natural to choose a town where to live. But there is no need for gated-cities in mathematics. We may work on a project with the goal of giving free full access to all mathematics to everyones. Of course, this is not “my” dream but the dream of many mathematicians of many generations. It was the dream of Bourbaki and also the dream of Eilenberg, MacLane and Lawvere. It seems to me that we should make a concerted effort to realise it now. Even a partial success may capture the imagination of the scientific community and of peoples in general. It will strenghten our confidence in the success of collective efforts. We need to develop this kind of confidence to fight the ecological disaster.

I believe that a project like the nLab is already moving in the right direction. Thanks to its active contributors! I would love to see it extended, deepened, multiplied, diversified and scaled up.

What do you think?

Best, André

end forward of old discussion