Re: CatLab

[Urs Schreiber <urs.schreiber@googlemail.com>]

Dear André,

thanks for your message.

You write

> The nLab is a very nice thing!

I am pleased to hear that you think working on such wikis may be
worthwhile! That's very encouraging to hear, from somebody like you.

The nLab is just a first, tiny and tentative step, but eventually,
with more work, this kind of activity could be rather useful, I
believe.

You write:

> Maybe you could create a wiki-lab for homotopy theory too (a HoLab?)
> Maybe all these labs could be connected.

Before I enter the technicalities of setting up separate wiki-labs
below, let me ask you one question:

as you indicate, one useful aspect of wiki material is its
interconnectedness, via hyperlinks. I am imagining that eventually,
with plenty of time, effort and contributors, a large web of
wiki-material will grow, covering many parts of math and exhibiting
their connectedness. For instance pure abstract category theory
entries may point to entries about physics where the concepts are
applied, and vice versa.

We currently think of the nLab as a wiki to encompass all that, in
principle -- being well aware, of course, that its current state is at
best just a puny approximation to what it could be, eventually.

So my question is: could you tell me what it is that makes you feel
that topics like category theory or homotopy theory need to be more
physically separated out of the nLab as a whole
(if that's what you feel)? Could't you see a useful way that they
exist as clusters of related entries inside the  whole structure?

This is at least currently the idea that we have:  when clusters of
entries corresponding to a given topic begin to accumulate, we
currently try to equip them with shared "floating tables of contents"
that give them a kind of sub-web existence within the nLab, without
losing the close contact to the rest of the web. Such sub-clusters do
currently include, among various others, the topics

category theory -- http://ncatlab.org/nlab/show/category+theory+-+contents
higher category theory --
http://ncatlab.org/nlab/show/higher+category+theory+-+contents

We don't have as yet a reasonable such cluster on homotopy theory,
though we have for instance the beginning of one on "abstract homotopy
theory", i.e.

model category theory --
http://ncatlab.org/nlab/show/model+category+theory+-+contents

As I said, none of this is meant to be anything close to perfect, it's
just to indicate seeds of possible structure within the nLab.

So my gut reaction to your question would be:

let's all improve and expand on the existing seeds of topic
sub-clusters within the nLab, such as notably those on category
theory! Let's not spread these efforts over too many different
software installations. The more they are connected by one single web
of links, the better.

All this said, here is a little non-exhaustive bit of information on
technicalities of setting up wiki-webs:

what is straightforward is to branch off separate "instiki webs", as
they are technically called,
from the nLab. All these webs work just as the nLab itself does, they
look and feel the same, and all run on the same software.

Currently we follow the practice of offering personal webs to
contributors who feel that they want to put material into the wiki,
but in a more personal or private way than on the main nLab web. You
can see the list of all sub-webs that current exist here:

  http://ncatlab.org/web_list
  http://ncatlab.org/nlabmeta/show/directory+of+personal+webs

It is very easy to create such a sub-web titled "category theory" or
"homotopy theory" or the like.

If you do tell me that you would be likely to start adding material
on, say, category theory, to such a sub-web "category theory", while
not as likely to add the same material within the nLab web as such, I
will be sure to take care that such a sub-web is created soon. But in
that case, maybe we could jointly try to think about what would be
necessary requirements, from your point of view, to instead keep all
the material within the nLab itself.

You see, in practice the main difference between two entries within
the same web and two entries on different webs is, apart from maybe
the color scheme of the entry header, just that hyperlinks within one
web are easily and conveniently created -- one just types
"[[keyword]]", while hyperlinks across webs are more tedious,  one has
to type "[[webname:keyword]]". The user who views these pages may not
even be able to tell the difference, though!


Finally, it is of course also possible to set up entirely separate
installations of the wiki software. We are very lucky to have Andrew
Stacey among us, who has the expertise and energy to handle such
things. He is our software administrator, if you wish. Originally
Jacques Distler helped us with these matters, but he is rather busy
with lots of other things. If you think you would want an entire
separate software installation of the wiki software on some server,
then you should ask Andrew Stacey about this. If I remember well, he
is already running a second wiki installation of the nLab kind for
some other purpose.

With best regards,
Urs

On Wed, Dec 23, 2009 at 8:10 PM, Joyal, André <joyal.andre@uqam.ca> wrote:
> Dear Urs,
>
> The nLab is a very nice thing!
>
> http://ncatlab.org/nlab/show/HomePage
>
> You wrote:
>
>> It is a wiki-lab for collaborative work on Mathematics,
>> Physics and Philosophy —especially from the n-point of view:
>> insofar as these subjects touch on higher algebraic structures.
>
> The nLab is devoting a lot of space to category theory.
> It would be nice to have a CatLab devoted to category theory per se.
> Is this something that can be created ?
> My knowledge of wiki-technology is null.
> Maybe you could create a wiki-lab for homotopy theory too (a HoLab?)
> Maybe all these labs could be connected.
>
> Best,
> André


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]